Answer the below:
Q1) Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.
a) What is the probability that you will receive a Merit scholarship?
b) Are events A and M mutually exclusive? Why or why not? Explain.
c) Are the two events A, and M, independent? Explain, using probabilities.
d) What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?
e) What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?
Q2) In the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55. The probability that UTC will defeat both opponents is 0.3465.
a) What is the probability that UTC will defeat Furman given that they defeat Marshall?
b) What is the probability that UTC will win at least one of the games?
c) What is the probability of UTC winning both games?