Question

A student is applying to Harvard and Dartmouth. If the student is accepted at Dartmouth, the probability of being accepted at Harvard is 40%. If the student is not accepted at Dartmouth there is an 80% of non-acceptance at Harvard. There is a 50% chance of being accepted at Dartmouth. What is the probability a student is NOT accepted at either Harvard or Dartmouth?

Answer 1

Let Harvard and Dartmouth be represented by H and D respectively.

Then, we are given here that: If the student is accepted at Dartmouth, the probability of being accepted at Harvard is 40%, therefore we have here:
P(H | D) = 0.4

Also, we are given here that: If the student is not accepted at Dartmouth there is an 80% of non-acceptance at Harvard,
Therefore P(not H | not D) = 0.8, therefore P(H | not D) = 1 - 0.8 = 0.2

Also, we are given here that: There is a 50% chance of being accepted at Dartmouth, therefore:
P(D) = 0.5

The probability that the student is not accepted at either Harvard or Dartmouth is computed here as:
= P(not H | not D)P(not D)

= 0.8*(1 - 0.5)

= 0.4

Therefore 0.4 is the required probability here.