00:01
The probability that a box of cereal has a prize in it is 0 .2.
00:06
And we're going to purchase box after box until we've collected four prizes.
00:12
And the random variable x is the number of boxes until we get four prizes.
00:17
And it was already identified in part a that x is a negative binomial random variable based on four successes, and probability of success, 0 .2.
00:29
And for part b, we want the probability that we will purchase six boxes to get the four prizes.
00:38
Now generally the probability mass function for a negative binomial random variable is given by this formula.
01:07
So we are looking for the probability that it takes exactly six drives.
01:13
So using the probability mass function, we have 5 choose 3 times 0 .8 to the exponent 2 times 0 .2 to the exponent 4.
01:30
And this comes out to 0 .01 approximately.
01:37
And then for c, we want the probability that we purchase at most 6 boxes to get 4 prizes.
01:43
So this is the probability that x is less than or equal to 6.
01:49
Now let's use excel to solve this.
01:51
Excel has a negative binomial distribution function.
01:55
So in excel we start with an equal sign.
01:58
We find the negative binomial distribution function highlighted here in blue.
02:01
So we select that.
02:04
So if we consider getting the four prizes in six trials, we would have to have two failures...