You have applied for two scholarships: a merit scholarship (M) and an athletic scholarship (A). Assume the probability that you receive the athletic scholarship is 0.25, the probability that you receive both scholarships is 0.15, and the probability that you get at least one of the scholarships is 0.37. Use a Venn diagram to answer these questions:
a. What is the probability that you receive the merit scholarship?
b. What is the probability that you do not receive either of the two scholarships?
c. What is the probability that you receive the merit scholarship, given that you have been awarded the athletic scholarship?
d. What is the probability that you receive the athletic scholarship, given that you have been awarded the merit scholarship?
e. Are the events “receiving an athletic scholarship” and “receiving a merit scholarship” independent events? Explain.