Anindya Madhudor wrote:The acceptance rate at a certain business school is 15% for the first time applicants and 20% for all re-applicants. If David is applying for admission for the first time this year, what is the probability that he will have to apply no more than twice before he is accepted?

a. 2/31
b. 3/19
c. 8/25
d. 1/17
e. 33/100

OA: C

For probability questions, I always ask, "What needs to happen for the desired event to occur?"

In order for David to apply no more than twice, it must be the case that either he is accepted the 1st time OR denied the 1st time and accepted the 2nd time)

P(apply no more than twice) = P(accepted 1st OR denied first and accepted 2nd)
= P(accepted 1st) + P(denied first and accepted 2nd)
= 15/100 + (85/100)(20/100)
= 32/100 = [spoiler]8/25 = C[/spoiler]

Cheers,
Brent