00:01
The scenario that we're given in this question is that a basketball player makes 80 % of his foul shots.
00:08
And we can assume that shots are independent.
00:12
So this suggests to us that each foul shot is a bernoulli trial because each shot is independent from the other shots.
00:19
And we know the probability of success is to be 80%.
00:23
And there's only two outcomes.
00:24
There's either success or a failure.
00:29
Now in part a, we were asked, what is the probability that the player misses for the first time on his 50 %? attempt.
00:37
So if we're counting the number of shots until we have a miss, it's easiest if we count the miss as a success.
00:46
So x is the number of trials until success.
00:59
This is our random variable.
01:03
And p is the probability of success, which is 0 .2 because we're counting misses as success.
01:11
So x is a geometric random variable.
01:14
It's number of trials until success for bernoulli trials.
01:20
So to find the probability that the player misses for the first time on his fifth attempt, you can say probability x equals 5 is equal to a geometric random variable for five trials based on probability of success of 0 .2.
01:53
So this is equal to 0 .8 to the exponent 4 times 0 .2 .2.
02:03
So this means that we have four failures until the one success...