Astudent 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?

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%