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Hello my name is Beth Dixon and this is a video series
based on Vicki Borlaug's PowerPoint presentation
on Law of large numbers I wish to thank Mrs. Borlaug for allowing me to use her
PowerPoint presentation to make this series of videos on probability
Mrs. Borlaug designed this particular PowerPoint presentation to be used after her
class had done an in class activity using beads and the handouts that you see on your screen
I will make this video balancing the fact that some of my viewers have done this activity while most probably have not done the activity
the major concepts should be the same either way
before we began I will need to introduce some terminology that we will use
as I've said in the previous videos terminology and vocabulary are a big part of a probability and
statistics course and you will need to pay attention to the language and verbiage
that your instructor uses
flash cards are a great way to learn any new vocabulary
our first word is experiment
an experiment is a process by which we get
results called outcomes
from the population
to help with this terminology we will start with an example
in this case a population of 45 cars in a parking lot
and experiment from this example might be to select one car at random
next outcome
an outcome is a result from an experiment
from the experiment our outcome
is a particular car that particular car that we selected at random
for example the car in parking space number 37
an event is a collection of outcomes
the event R would be a red car
so once we have selected a car we have that outcome and then we would check to see if it is a red car
we might check to see if it's a Toyota is the car I selected a Toyota
does the car have a sunroof Event S might be a car with a sunroof
a simple event is an outcome
that is a single result the red Lexus and parking space number 12 would be considered a simple event
sample space
all possible individual results from an experiment
so our sample space would be the 45 cars in the parking lot
now it is time to look at another example
our population consists of 30 students of whom 9 are wearing sneakers
were going to run an experiment where we will select one at random and then put it back
our sample space consist of the 30 students and our event is wearing sneakers
first we will discuss the classical approach
the classical approach
is based on population information
and to find the probabilities
using counting it will only work
if the simple events are equally likely
to find probabilities using counting only works
for equally likely simple events
so what would the probability of selecting a student wearing sneakers be
I like to draw a picture of my data or represent my data in my own handwriting so oftentimes I will create a table
or a chart or even just jot down the numbers so that I know what the numbers are
so taking the information from our population
I will say that we have equally likely simple events selecting any one of the students is equally likely
we have nine with sneakers for a total of 30 which will leave 21 without sneakers and by making this table or chart here I have
taken the information and put it in a way that I understand it so what is the probability of
selecting someone with sneakers well it would be the nine with sneakers out of the total of 30
nine out of 30 or .30
this is called the true probability
next we will discuss
the relative frequency approach or an empirical approach
the empirical approach is based on what
it's based on repeating the experiment
so we're going to pretend that we've run the experiment that I've run the experiment and will say that I ran it 48 times
and each time I ran the experiment I look to the student said are you wearing sneakers
got a yes and no response and put the student back into our population
and I counted the number of times I got a student with a pair of sneakers and that was 13 times
then by using relative frequency
I can find the probability of sneakers from my experiment was 13 out of the 48 times I
selected the students the student was wearing sneakers which gives me 0.2708
and this is called the relative frequency
this is an estimate of the true probability
if I ran the experiment 48 times again I could get sneakers a different number of times the total would still be 48 but I might get
more than 13 I might get less than 13 as the number of sneakers
that I counted
here is as sum of the two approaches or summary of the two approaches
my estimate the relative frequency under a estimates that through probability
will it always be an underestimate
think about that remember I said I could get more than 13 sneakers or less than 13 sneakers we will look at this more in part two of this video
series
before we move on and as we conclude part one here are some formal definitions of the two approaches
in the classical approach a population must consist of equally likely simple events
then the probability of A is the total number of ways a occurs
divided by the total number of outcomes
let me say that again the probability of A is equal to the number of ways A can occur divided by the total number of outcomes
the relative frequency approach or empircal approach the same experiment is repeated
and the probability of A is the number of times a occurs
divided by the total number of times
the experiment is run
an experiment such as select one at random
and in the law of large numbers if the experiment is repeated over and over again the blank approaches the blank
and using the words true probability and relative frequency
what do you think happens
the relative frequency approaches the true probability
I will end the first video
of this set here if you would like more help with this topic please watch the second video of this
series and as always Walter State students are welcome to stop by and see me in MBSS 222