The acceptance rate at a certain business school is 15% for first time

Question

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

A) 20%
B) 30%
C) 32%
D) 35%
E) 40%

Show Answer

Official Answer

C

A) 20%
B) 30%
C) 32%
D) 35%
E) 40%

TaizKaran · Accepted Answer

Let's suppose that he gets into the school in his 1st attempt. The probability is 15/100. We don't need to consider the 2nd case because he has already gotten into the school.

So the 1st case is 15/100 -------1)

In the second case he doesn't qualify in the 1st round which means probability is 85/100. We'll multiply it with 20/100 because he is supposed to clear it in his 2nd attempt.

The second case is 85/100*20/100 = 17/100-------2)

On adding 1) and 2) we get 32/100= 32%

GMATSheep · Answer

The question is asking the probability he will be accepted after two submissions. This is the same as 1 - (probability he gets rejected twice). Probability of two rejections = (85/100) * (80/100) => 68/100, thus 1-(68/100) = 32/100 => 32% is the answer.

AnirudhaS · Answer

P(Accepted at No more than 2 tries) 
= P(accepted at first try) + P(accepted at second try)
= 0.15 + (1-0.15)*(0.20)
= 0.15 + (0.85)*(0.20)
= 0.15 + 0.17
= 0.32
Probability is 32%

Answer: C

Shivm44 · Answer

Hi everyone!

Can anyone please clear-up how the probability for acceptance for the 2nd time applicant is 17%? 
Why is it different from 20% in the first place? I see that its is being calculated on 85% which is the (1 - 0.15) from the first application, but what is the reason for that?

Thanks 
Shivam

Crytiocanalyst · Answer

Second time it becomes 85/100 * 20/100 = 17 /100

hope it's clarifies

RahulJain293 · Answer

I solved it as below without prior knowledge of the topic: (took me 1:07)

Assume we have 100 candidates who apply to the college
Round 1 - Only 15% ie., 15 candidates are selected.

Meaning 85 are not selected in Round 1.
Now assuming all 85 reapply; Round 2 we have 20% of 85 who are accepted ie, 17.

In total, we have 15+17 = 32 candidates selected from an overall pool of 100 after reapplying (or applying twice)

Hence 32% would be the probability that he would not have to apply more than twice to be selected

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The acceptance rate at a certain business school is 15% for first time

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