Excel 2013 Statistical Analysis #25: Probability Basics: Sample Points, Events & Event Probabilities

Download files: http://people.highline.edu/mgirvin/ex...
Topics in this video:
1. (00:12) Review Handwritten PDF Notes about Probability, Random Events, Sample Points, Sample Space, Count Rule For Size of Sample Space, Listing all Sample Points with Tree Diagram and Table, Methods of Probability such as Classical, Relative Frequency and Subjective, Requirements for Probability, Events and Probability of Events
2. (14:30) In Excel: Experiment of Flipping Coin Three Times: Find all Sample Points, Calculate Probabilities and practice finding Probabilities of Events by listing all the sample points and then adding all the probabilities for each Sample Point to get the Probability of the Event
3. (21:09) Frequency Distribution Built from Sample Space in order to find Probabilities for Events
4. (23:46) In Excel: Experiment of Rolling Two Die: Find all Sample Points, Calculate Probabilities and practice finding Probabilities of Events by listing all the sample points and then adding all the probabilities for each Sample Point to get the Probability of the Event

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Closed Caption:

welcome to exhale 2013 statistical
analysis video number 25
hey if you want to download this excel
file and the PDF file that goes along
with chapter 4 click on the link below
the video I'm going to do some unusual
this will be the first time or might not
using excel i have these handwritten
notes it's a PDF file that you can
download these are the notes just like i
would write them on the board in class
now we're going to talk about the basics
of probability so I have some
handwritten notes here but then we'll go
over to excel and do a bunch of
calculating now probability what is
probability well the synonyms for
probability chance likelihood
possibility
anytime you hear people use those words
we're talking about a number between 0
and 1 greater than or equal to 0 or less
than or equal to 1 it can never be
anything above one or anything below
zero you know tests and quizzes in this
class I get people to give me minus
numbers in huge numbers above one just
remind yourself
those are not probabilities because you
think about it if something if we're
given a probability that something can
happen the biggest number it can ever be
is I'm a hundred percent sure it's going
to happen you can't have a hundred and
ten and 0
there's a 0% chance that event will
occur
those are the two bookends 021 inclusive
now probability is a chance that
something will occur in the unknown
future now even if we create a
probability and we're pretty sure about
it it's still only an estimate our
probability is never known with certain
certainty
it's only an estimate now we're going to
talk a lot about probability but we
gotta start with a bunch of terminology
how about random experiment random
experiment we're going to have three
important points the first a process
that generates well defined outcomes so
for example if your toss in a corn you
either get heads or tails
there's no other possibility driving on
a bridge and you're interested in
traffic
you either get stuck in traffic or you
don't get stuck rolling two die there's
only six possibilities a product coming
off of an assembly line
it's either defective or not defective
the next . on any single repetition one
and only one of the possible
experimental outcomes can occur so if
the product comes off the line
it's either defective or not affected it
has to be one of those third the
experimental outcome that occurs on any
trial is determined solely by chance so
that's our random experiment now going
to see a lot of experiments but most of
them are going to be multi-step that
just means more than one step right
rolling a die 2 times flipping a coin
three times or driving across the bridge
seven times and we want to know what's
the probability of getting and stuck in
traffic 0 or 1 or 3 times so multi-step
experiment now when we do experiments
one of the basic building blocks of
learning probability is the sample . and
we're going to do a lot of trying to
figure out what all the sample points
are when we run experiments sample point
is simply one of the possible
experimental outcomes and these two
words are synonyms sample . experimental
outcomes and the textbook in in my notes
in Excel and when i talk i tend to use
them interchangeably i'll try to use
sample . more than anything
now examples of a sample . what if we
flip a coin one time well it's either
head or tail say . one head sample point
to a tail but when you start having
multi-step signore experiment then it
gets tricky sometimes sometimes it's
about
possible list all the sample points but
let's look at this flip a coin to x
well one of the possibilities we get
head another possibility as we get head
tail still another is tail head and
finally the fourth one would be tail
tail a lot of times people get these
middle two mixed up and they'll only
counted as one now figuring out and
listing all the sample points will do
that on some small data sets but for big
data sets it gets pretty difficult will
also see a method to determine how many
actual sample points there are in a
sample space what's the sample space
Oh sample space it's a list of all the
possible experimental outcomes so for
example for our first just flipping a
coin once RS would be HT now what if we
flip a coin to $OPERAND times the sample
space would be well head head head tail
tail head and tail tail now sample
points like this when we doing we're
also going to calculate the
probabilities for each one which will
help us figure out some of the tougher
probability problems now our formula for
counting is going to be pretty
straightforward total number of
experimental outcomes sample points
right we need to figure out all the
sample points
it's just going to be outcomes on step
one outcomes on step 2 all the way to
the final step
k will be our number of steps like
flipping a coin twice k would be two and
one would be too because we have two
possible heads tails and number two
would be heads tail now if the number of
possible outcomes is the same each time
we can simply take whatever the number
of outcomes raised to that total number
of trials here's two examples flip a
coin three times well its end 22 and why
because we get head tail head tail heads
or tails
so three steps multiply 2 times 2 times
to get a tour because and is the same
each time number of outcomes we can
simply go to the third how about for
rolling a die 2 times well we have six
possible
outcomes and then on the second roll we
have still six possible outcomes so if K
is to again this is the same possible
number of possibilities for each end so
we simply can't say six raised to the K
which is 36 and we'll do both of these
examples now in our next video we'll
talk about combinations and permutations
i'm going to skip over these now listing
all the sample points in the sample
space we have a couple ways we can do
this one is the tree diagram so far
experiment is tossing a coin three times
well we start with the first toss header
tail and then we go when we get to this
point right here what we get head tail
then we get to this point right here
head tail so only on this outside tail
tail tail that tells us one of the
sample points tail tail head there's
another sample . tail head tail still
another sample . and the tail head head
that's a fourth sample . so you continue
this tree diagram and you can list all
of the sample points you can also lists
all of the probabilities and we will see
how to do that another way to do this is
the table format
step 1 2 3 4 our experiment and then you
have to methodically list head head head
head tail etc and we will actually do
this one over in Excel now are our next
example would be are rolling a dice and
notice we're going to use the table
format here list 126 126 and then the
intersection
you could also do this one vertically
but sometimes easier to list it like
this
now the interesting thing about listing
sample points is you're like wow that's
crazy but check this out what is six and
one it's seven right
what is five and 27 each one of these is
a role of rolling two die right for
three so we gotta 4313 and for each one
of these adds up to seven so here's the
deal in probability if you want to know
the probability of Rome
Lena seven you have to look at the
sample points and count how many there
are six and / r36 that will give us the
probability of rolling a seven now it's
not always this easy and we'll see some
examples like with conditional
probability where it's not straight
counting and dividing by the account but
again listing all of the sample points
as you're learning probability is really
helpful for understanding how
probability works now methods of
assigning probability three basic
methods the classical method that's like
flipping a coin or rolling the dice all
experimental outcomes are equally likely
that's the definition of our classical
method in that case we can simply count
the number of favorable sample points
like dice add up to seven and $OPERAND
divided by the total number
another example here if you get audited
by district office
well that district office does three
million tax returns and they always
audit 3000 well if you know that then
you can simply do the straight division
and you get one out of a thousand that's
the probability that you're going to get
audited using the classical method now
the next method relative frequency oh
we've already talked about this
that's doing our frequency distribution
and then relative frequency with
formulas or pivot table from a data set
those decimals or percentage are our
relative frequencies the idea of
relative frequencies we use past data to
predict the future now the law of large
numbers which I kind of wrote sideways
so you have to turn your head off to the
side here over a large number of trials
relative frequency will approach the
true probability and that sort of makes
sense right if there was a thousand in
the population the closer and closer
your sample size gets to a thousand the
more your relative frequency method of
estimating the probability gets to the
true probability the final method is the
subjective method
and there's a couple ways you know that
you're doing subjective right you can't
realistically assume that all outcomes
are equally likely and there's little
past data now I'm actually shooting this
on january $MONTH thirty-first 2015
which is the night before the superbowl
between the seahawks and the Patriots
now you think you could look at past
data and figure out the probability but
i don't think so
I mean think about it russell wilson and
quarterback for the Seahawks Tom Brady
quarterback for the Patriots the coaches
Carol and belcheck all the players well
wait a second they've even played before
right
but all of the details were different
the last time they play the location
that they're playing down in Arizona
it's all different
so there's really no past data you can
look at things that are parallel and try
and estimate but once you do that you'll
be using the best information you have
but it will be your personal belief
alright so we have classical relative
and subjective now a couple more
important points before we jump over to
excel requirements for assigning
probabilities guess what every
probability is going to have to be
between 0 and 1 inclusive oh well we
already talked about that but think
about our relative frequencies right
each one of the individual items was
between 0 and 1 inclusive and all of
them together had to add up to one and
that's going to be true for every one of
our situations when we're assigning
probabilities and we'll do a bunch and
every time will check is each individual
probability between 01 and are the
totals of all those probabilities adding
up to one now two last points we have to
learn what an event is and how to
calculate the probability for an event
now and if n is simply a collection of
one or more sample points now think
about our dice example right we had to
count how many sevens there were that's
a collection of one or more sample
it's and the event was rolling a seven
calculating the probability of event
well we did that to remembers 6 / the 36
gave us the possibility of getting a
seven when we roll two dice let's scroll
down here look at another example and
will actually do this a bunch
here's our experiment tossing a coin
three times one two three lists all the
sample points and look at this since its
classical each sample point is simply 18
or 0.125 but if we're talking about
events the event of two tails in three
flips will guess what there's three
sample points if we're going to
calculate the probability what is the
probability we have to add up the
probability for each sample . down here
we have our sample points 1 2 3 and here
we have . 125 + . 125 + 1.125 and we get
played 375 so if you roll a pair of dice
and you're expecting to get a 7 you can
estimate using classical probability
that the probability is . 375 now I want
to jump over to excel and talk about all
of the terms we just talked about and do
some examples now we're on the sheet all
sample points here's our multi-step
experiment flip a coin three times K
that's the number of steps or trials and
so we're going to type of three number
of outcomes
well it's either heads or tail for the
first one how about the second one
oh it's still heads and tails how about
the third one nuts heads and tails its
they're not always the same but in this
case they are so simply the long method
simply sick and one number of outcomes
times n2 number of outcomes x + 3 number
of outcomes and we get 8 or because each
step has the same number of outcomes we
simply take one of these and raise it to
the number of steps or
trials are k so eight alright so i'm
going to list 1 through 8 12 enter now
watch this i'm going to do a culture i'm
going to highlight one and two . to the
fill handle when I see my angry rabbit
click and drag on there i get 128 now
this is the hard part right
hey we'll step one step two step three
we're gonna have to list all the sample
points well I'm gonna go head head head
that one's easy now I'm going to since
this is the only one with three heads
the next one is to head so I'm gonna try
head head and tail
ok well the tails at the end now i'm
going to put the tail in the middle and
then put a head here and ahead here now
there's a tale a tale so now i'm going
to put a tail there and then this will
behead head
alright well okay so we got three heads
two heads now this is one so I'm gonna
start off with one and then a tail tail
ok so I've ahead in the beginning so now
i'm going to put head in the middle and
then this one's a tail and that was the
tail and then had had so i'm going to
put one at the very end so that makes
these tales and the last was simply tail
tail tail now if we're listing the
sample space and sometimes we'll have to
do that all the way up through chapter
on seven or 8i think when we do the
central limit theorem you can either
type this out
h comma 8 comma h or we can build a text
formula you don't have to do this but
i'm going to show you how to do this
well the first thing i want is I want
the equal sign remember we have a join
operator in a percent and then I need to
put the comma in double quotes and I
want to space so i actually have in
double quotes comma space now i need to
join that to the next one book and I'm
going to cheat i'm going to copy this i
got that perfect setup copy ctrl c and
control via that i can click on the last
one and that'll work all the way down
and copy it down that's perfectly fine
if you wanted to have the parentheses
and sometimes you want to do that then
you could put double quote open paren CW
quote and join notice how when the
formula is not working they'll turn
black or everything after the error and
then at the end I'm going to join and
double quote close parentheses in double
quote control-enter and copy it down
alright so now we calculate the
probability well this is classical
probability so I'm simply going to say
what equals 1/8 f4 control and term and
copy down later we'll have examples what
we're doing probability for sample
points and it will not be that will have
to do some tricky formulas with
conditional formatting alright so now
hey let's check out rule number one or
all of these between 1 & 0
yes so our first requirement for
assigning probabilities that has been
met now what about this i'm going to alt
equals and enter that equals 1 so
requirement one each one of these is
greater than equal to 0 on less than or
equal to 1 and then down here that some
of them are one now let's put this to
use i'm going to scroll down here we're
going to and try and calculate some
probabilities
hey the first probabilities hey what's
the probability of three straight heads
while looking at our sample points we
can see there's only one so here I could
just go 1/8 or I'm gonna . up there and
get that probability from the table
remember the definition of an event well
there's the event pull three straight
heads and there's the sum of all the
sample points now i'm going to list the
sample . right here because again we
want to emphasize that probabilities of
events are finding all the sample points
the probabilities and then adding them
now what about our next one probability
of two tails and three tries well I
gotta go up to my sample points
it looks like tail tail tail tail and
tell so these three right here i'm
actually going to list these first ready
equals hey there's a head tail tail tab
equals tail head tail tab equals
telltale head boom there's our three
sample points now I'm going to add the
probability for those sample points alt
equals group and enter now again for
classical we could count and / the count
but we're emphasizing because later
we're going to as we're learning try on
the tricky ones to figure out the
probabilities for each sample . and then
Adam all right our last probability
probability of one tail and three tries
all that's up here there's one tail
one-tail 12 so these three right here
I'm not list all the sample points
head head tail tab equals head tail head
tab equals tail head head tab each one
of those has one tail and we're going to
alt equals the definition of
probabilities to add up the
probabilities for those sample points
and there they are
enter now we want to go from this
example here we're adding up sample
points but in a situation like this we
can actually find all of the tues right
two tails and three tries we can
actually find all of these probabilities
an atom in a table so let's go over 20
RF table
sounds like a relative frequency table
now notice what I did over here is
here's the table we just built but I
went ahead and added a formula conex and
I'm counting the t's that's a relative
cell reference right so as I copy it
down accounts so here's a list right
next to our sample points and our sample
. probability we have the number of and
it's not heads its tail's we've defined
a success up here
as a tail so that was the wrong label
there but 0112 23 so now let's come over
here is our frequency table remember the
first column has a unique list 3210 now
we count then we calculate the
probability so frequency equals count
ifs and the criteria range that's what
this whole range right here
f4 to lock it come up one cell to my
left there's the criteria for counting
so three we better get a count of one
when i copy this down 331 absolutely
beautiful now when we add these
frequencies up all 2 equals we better
get the total number of sample points
and sure enough we do we don't need to
add but now we need to calculate
relative frequency equals 0
there's the frequency just as we did in
chapter 2 / the count f4 control enter
each one of these better be between 0
and 1 inclusive they are and when we add
them up
alt equals that going to be equal to 1
both requirements are looking good now
we have our probabilities here and when
we come and ask a question pull three
straight heads we can simply say equals
well there's the probability for pulling
three straight heads probability of two
tails in three tries equals I just click
on there's the two we've already added
them up boom probability of one tail and
three tries there it is
next chapter will see this is a random
variable will call it X there it is so
equals there's the probability
associated with this event and enter now
we want to go look at our third example
on all sp2 now on this she will want to
try to list all the sample points for
the experiment rolling two die now we're
going to have the dice in our hand and
thrown at the same time but all really
be one and then the other that means
there will be two steps or trials six
sides on each die
that means there's 36 total sample
points we simply took six square now I
want to list all the sample points and
it seems like a lot but we'll see some
cool tricks to make this go quickly
the first one is and we saw this last
example 1 enter 2 enter and i'm going to
highlight both and notice when I point
to that fill handle and my selection
cursor turns to an angry rabbit
click-and-drag now notice what this does
this increments the numbers it's called
a series we're adding by one so we get
all the way to 36 now if we're going to
list all of the sample points we need a
11 21 31 etc so over here I'm gonna do
one to highlight and i'm only going to
copy it to 610 sits incrementing put
watches since I want to repeat 126 126
126 many times
double click and send it down because
there's something to the left goes all
the way down but it's doing a series its
incrementing the numbers but watch this
little smart tag i'm going to click on
it that little arrow and see
copy the cells instead of the default
fill series so copy 126 126
not-so-pretty culture now watch this we
do another trick highlight and i'm
highlighting all six next 21 26 that
active cell i'm going to type a1 now
notice it's in edit mode and I put
something in the active cell if I
control-enter will populate all the way
down ctrl enter now i can come down
highlight the next six to control enter
the next 63 control enter the next six
the active cell i type of for control
enter 5 control-enter six control-enter
that's pretty cool that was fast it
seemed like 36 sample points would be a
lot but we did it quickly now I
definitely want to list the sample
points and we're going to just like we
did before our texts equal sign
double quote open parenthesis double
quote and I'm gonna join that to this
one
control-enter and double click and send
it down you can see that gives us just
those two things joined f2 I need to
join it in double quotes comma space and
double quote and join it with the next
role and finally I need to join it
ampersand double quotes and I need a
parentheses and double quote
control-enter double click and send it
down
that is pretty cool that's a lot faster
than doing it by hand by the way not
only is it faster doing it by hand but
you're going to avoid errors inevitably
if you have to type all this out you get
some errors that's why even over here
having some tricks to enter that data
was very helpful
now we want our probability hey this is
a classical example each one of these is
one we simply take 1/36 and that gives
us the probability for each sample point
equals 1/36 and I'm gonna at four
control-enter double click and send it
down now if we're going to ask
probability questions about the sum of
these let's just add them up
alt equals it guesses wrong but the
dance and answer moving so we simply
redirect it
those are two relative cell references
control-enter double click and send it
down any cell f2 you see it works
perfectly
that's pretty cool look at that 2347 all
the way down now it looks like there's
only going to be 12 and 1 12 but all the
rest of them will have some repeats like
33 a look that snake eyes 11 the only
get one snake eyes
now we can do our probability hey what's
the probability of something 22 it's
simply one sample . there's the
probability tab I'm going to come over
here and list the sample . alright
that's pretty cool now how about the
probability of getting off
war meaning the summer for well let's
see there's a 44 a full down here
whoa so there's no more down there so
watch this i'm going to list them equals
there's the sample . tab equals i'm
going to be careful how i'm doing this
manually right tab equals and i'm
scrolling down there it is right there
tab now why are we believe bring all
this because really listing sample
points getting the sum the total is
really going to help us throughout this
chapter next chapter and i'll be the
foundation of the understanding
probability for the rest of our chapters
hey i'm going to add them up equals poop
plus there's a 4 here plus and I know
these are all the same but i'm just
getting idea i'm adding these different
and later they won't be the same
we'll see some examples with conditional
probability hey there we go . 083 so
eight and a third percent now
1111 way down at the bottom i'm going to
say $OPERAND equals and scroll all the
way down i'm looking for 11 look like
there's 12 so just gonna get that sample
. tab equal and scroll down tab
alright and so then adding them equals
scroll all the way down so there's the
11 there's the probability i'm gonna
type A+ you can see it coming up in the
formula bar and then there's a plus
right there
and enter so there we have listed all of
the sample points for rolling two die we
actually added them all up and then we
saw again that when we have an event
like the sum of two of the sum of four
oftentimes we're having to list multiple
sample points and then add up the
probabilities
alright so for this video we talked
about the basics of probability and most
importantly we talked about sample
points and creating a sample space
getting the probabilities we talked
about events and getting the probability
for events which means finding the
sample points adding up the
probabilities next video we'll talk
about combinations and permutations and
then after that we'll continue our study
of calculating probabilities for events
all right we'll see you next video