Hypergeometric probability distribution?

Keith's fllorist has 15 delivery trucks, used mainly to deliver flowers and flower arrangements in the turlsa area. suppose 6 of the 15 trucks have brake problems. five of the trucks were selected at random to be tested. what is the probability that 2 of those selected have brake problems?





plz show how you got the ansewers so that i understand? thanks

Hypergeometric probability distribution?
Solving Hypergeometric Probability Distributions is relatively easy. The hardest part is deciding what to consider success and what to consider failure. I'm going to use finding a truck with a brake problem a success! (Failed brakes = success, Good brakes = failure)





Remember, the denominator is finding the total number of combinations that you could choose 5 delivery trucks from the population of 15. 15C5 = 3003





The question asks to find the probability of when selecting 5 (sample size) we will have exactly 2 to be successes (faulty brakes)...





To find the numerator of the probability, we need to find out the number of combinations of both selecting 2 out of 6 trucks in the population that have faulty brakes 6C2 = 15


Then we need to multiply that to see how many different combinations will give us 3 (out of sample of 5) to have working brakes. If there are 9 in the population, we only need three. 9C3 = 84





So...





P(x) = 15*84/3003 = 0.4196





Hope that's clear enough!