00:01
So we're told that computer chips from a certain supplier have a 7 % chance of containing a defect.
00:13
And then we're going to continue to test chips until we find 10 good ones.
00:25
And we're going to call x a random variable.
00:28
And this is the number of defective chips that we need until we found the 10th good chip.
00:33
Number of defects until this 10th chip, this 10th good one.
00:44
All right.
00:48
So this is the distribution.
00:49
This is a negative binomial distribution.
01:00
And this models the number of failures before specified number of successes occurs.
01:06
And so this is the function, and this is written as you'll see it in some textbooks, but this is where the variable is k, where k would be the number of failures.
01:19
R here, so k is number of failures, just like this, x or defects i guess.
01:27
R is the number of successes.
01:31
Which is r, number of successes.
01:36
And in this case, a success is 10.
01:39
We want 10 successes.
01:41
So in this case, we want r to equal 10.
01:44
P in this case, p is the probability of success.
01:54
And we know the probability of failure is 0 .7, probably the defect is, or as you me, is a proportion in 0 .7, or probability 0 .7.
02:03
So in our case, this, our p is equal to 1 0 .07, excuse me, minus, which is equal to 0 .93...