00:01
For this exercise, we are told that the probability that john will hit a target on any shot is 0 .4.
00:09
And he shoots at the target 10 times.
00:13
And we are asked for the probabilities that he hits the target exactly three times, and that he hits the target at least three times.
00:20
So let's define a random variable here as x as the number of hits of the target in 10 tries.
00:28
Here, each of the 10 attempts can be thought of as bernoulli trials having two outcomes of interest.
00:33
Either hits the target or not, and if we can assume that their outcomes are independent, then the number of successes in a fixed number of independent brunali trials is a binomial random variable.
00:46
So here, x is a binomial based on 10 trials, and probability success, 0 .4.
00:53
The probability function for the binomial random variable is given by this formula, and so for part one, we want the probability that he hits the target exactly three times.
01:15
This is the probability that x is equal to 3...