total of 1200 graduates of a university have gotten into medical school in the past several
years. Of that number, 1000 earned scores of 27 or higher on the MCAT and 400 had GPAs
that were 3.5 or higher. Moreover, 300 had MCATs that were 27 or higherandGPAs that
were 3.5 or higher.
If we randomly choose a graduate who got into medical school, define events:
A = scored a 27 or higher on the MCAT
B = had a GPA of 3.5 or higher
Find the probability of each of the following events.
a. A randomly chosen graduate who got into medical school scored below a 27 on the
MCAT.
Answer:P(AC) = 1 – P(A) = 1 – 1000/1200 = 1 – .833 = .167
b. A randomly chosen graduate who got into medical school scored a 27 or higher on the
MCATorhad a GPA of 3.5 or higher.
Answer:P(A or B) = P(A) + P(B) – P(A and B)
= 1000/1200 + 400/1200 – 300/1200 = 1100/1200 = .917
c. Are events A and B independent? Justify your answer.
Answer: No.
P(A) = 1000/1200 =