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- [Instructor] Anthony DeNoon
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is analyzing his basketball statistics.
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The following table
shows a probability model
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for the results from his
next two free throws.
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And so he has various outcomes
of those two free throws,
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and then the corresponding probability.
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Missing both free throws, 0.2.
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Making exactly one free throw, 0.5.
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And making both free throws, 0.1.
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Is this a valid probability model?
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Pause this video and see if you
can make a conclusion there.
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So let's think about what makes
a valid probability model.
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One, the sum of the probabilities
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of all the scenarios
need to add up to 100%.
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So we would definitely want to check that.
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And also, they would all
have to be positive values
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or I guess I should say none
of them can be negative values.
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You could have a scenario
that has a 0% probability.
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And so all of these look
like positive probabilities,
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so we meet that second test
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that all the probabilities
are non-negative,
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but do they add up to 100%?
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So if I add .2 to .5, that is .7,
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plus .1, they add up to 0.8
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or they add up to 80%.
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So this is not a valid probability model.
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In order for it to be valid,
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they would all, all the various scenarios
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need to add up exactly to 100%.
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In this case, we only add up to 80%.
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If we add it up to 1.1 or 110%,
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then we would also have a problem.
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We can just write no.
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Let's do another example.
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So here we are told you are a space alien.
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You visit planet Earth
and abduct 97 chickens,
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47 cows, and 77 humans.
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Then you randomly select
one Earth creature
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from your sample to experiment on.
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Each creature has an equal
probability of getting selected.
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Create a probability model to show
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how likely you are to select
each type of Earth creature.
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Input your answers as fractions
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or as decimals rounded
to the nearest hundredth.
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So in the last example, we wanted to see
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whether the probability model
was valid, was legitimate.
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Here, we wanna construct a
legitimate probability model.
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Well, how would we do that?
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Well, the estimated probability
of getting a chicken
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is gonna be the fraction
that you're sampling from
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that is our chickens because
any one of the animals
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are equally likely to be selected.
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97
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of the 97
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plus 47
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plus 77 animals are chickens.
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And so what is this going to be?
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This is gonna be 97 over.
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97,
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47, and 77,
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you add 'em up.
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Three sevens is a 21.
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And then let's see, two plus nine is 11,
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plus four is 15,
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plus seven is 22,
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so 221.
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So 97 of the 221 animals are chickens.
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And so I'll just write 97, 221s.
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They say that we can answer as fractions,
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so I'm just gonna go that way.
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What about cows?
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Well, 47
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of the 221 are cows,
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so there's a 47, 221st probability
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of getting a cow.
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And then last but not least,
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you have 77 of the 221s are human.
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Is this a legitimate
probability distribution?
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We'll add these up.
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If you add these three fractions up,
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the denominator's gonna be 221
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and we already know that
97 plus 47 plus 77 is 221.
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So it definitely adds up to one,
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and none of these are negative,
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so this is a legitimate
probability distribution.