00:01
We're looking at a collection of six computer chips.
00:03
Two of them are defective.
00:06
We're picking three for inspection, and we want to know how many defective chips are found.
00:12
We want to write out the probability distribution here.
00:15
So we have six chips, two are defective.
00:19
What we have here is called a hypergeometric distribution.
00:26
And the parameters that are interesting to us are capital n, population size, so the entire one.
00:32
Collection, that's six.
00:34
Capital k is the number in the collection who have a particular characteristic of interest.
00:41
That's two, the two defective ones.
00:44
And we also need lower case n the number we are picking out.
00:49
So the key here to find the probability that exactly x are defective is we make this fraction.
00:57
On the denominator we have all ways of choosing three chips, all combinations of three chips, because each of them is equally likely.
01:09
On the numerator, we have the number of ways that have x defective.
01:16
And that will tell us the proportion of ways we can pick chips that have x defective chips.
01:24
How do we know what these numbers are? or we go to combinations, the number of ways to pick things from a collection without replacement, where order doesn't matter.
01:38
And the formula from combinations, n choose r is n factorial over r factorial n minus r factorial.
01:46
But your calculator will have a button like this.
01:50
Okay, so we've covered what we need to solve this problem.
01:57
Let's make our probability distribution.
01:59
So we have values of x and the probabilities of them occurring.
02:03
What values might x take? well, it might take zero, no is effective out of the three, might take one, it might take two.
02:12
Even though we're taking three, it can't take the value of three because there aren't three chips to take...