SOLUTION: Assume that in the MPH steering committee there are 17 men and 24 women. Two members are chosen at random to serve in the internship committee. What is the probability of choosing

Algebra ->  Probability-and-statistics -> SOLUTION: Assume that in the MPH steering committee there are 17 men and 24 women. Two members are chosen at random to serve in the internship committee. What is the probability of choosing       Log On


   

Question 1014343: Assume that in the MPH steering committee there are 17 men and 24 women. Two members are chosen at random to serve in the internship committee. What is the probability of choosing two members at random and the first being a male and the second one being a female? Hint: assume you do not want to choose the same member twice; therefore, pay attention to the denominator.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
there are 17 men and 24 women for a total of 17 + 24 = 41.

the probability of the first person chosen being male is 17/41.

assuming that a male was chosen as the first person, the probability of the second person chosem being female is 24/40.

if the first person chosen was male, then there are 40 members left to be chosen from and 24 of them are female.

that's why the probability of the second person chosen being female is 24/40 rather than 24/41.

the combined probability is 17/41 * 24/40 = (17*24)/(41*40) = 408/1640 = 51/205 after simplificataion.

51/205 = .2487804878