Question

Ramon has applied to MBA programs at both Harvard and Stanford. He thinks the probability that Harvard will admit him is 0.5, the probability that Stanford will admit him is 0.5, and the probability that both will admit him is 0.2.

(a) Make a Venn diagram with the probabilitiesgiven marked.

(b) What is the probability that neither university admitsRamon?

(c) What is the probability that he gets into Stanford but notHarvard?

Answer 1

(a) The Venn diagram is attached below.

(b) The probability that neither university admits Ramon is 0.20.

(c) The probability that Ramon gets into Stanford but not Harvard 0.30.

Explanation:

Let's denote the events as follows:

H = Ramon gets admitted to Harvard

S = Ramon gets admitted to Stanford.

The information provided is:

P (H) = 0.50

P (S) = 0.50

P (H ∩ S) = 0.20

(a)

The Venn diagram is attached below.

(b)

Compute the probability that Ramon gets admitted in neither Harvard nor Stanford as follows:

`P(H^(c)\cup S^(c))=1-P(H\cup S) \\= 1 - [P(H)+P(S)-P(H\cap S)]\\=1-[0.50+0.50-0.20]\\=1-0.80\\=0.20`

Thus, the probability that neither university admits Ramon is 0.20.

(c)

Compute the probability that Ramon gets admitted in Stanford but not in Harvard as follows:

`P(H^(c)\cup S)=P(S)-P(H\cap S) \\= 0.50-0.20\\=0.30`

Thus, the probability that Ramon gets into Stanford but not Harvard 0.30.