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 accepted at both Harvard and Dartmouth?

Answer 1

I made a probability tree. Pls. see attachment. 

Based on the probability tree I made, below are the probabilities

Probability of a student accepted at both Dartmouth and Harvard is:
50% x 40% = 20%

Probability of a student accepted at Dartmouth but not Harvard is:
50% x 60% = 30%

Probability of a student not accepted at Dartmouth but accepted in Harvard is:
50% x 20% = 10%

Probability of a student not accepted in both schools is:
50% x 80% = 40%

As you can see, these probabilities total 100%