all Random Variables (Chapters 4-6) 200 points 4. Assume you have applied for tw

Question

all Random Variables (Chapters 4-6) 200 points 4. Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you will receive a n Athletic scholarship is 0.50. The probability of receiving both scholarships is 0.35. The probability of gettingateast 1.00. [12 points a. What is the probability that you receive a Menit scholarship? b. Are the events A and M mutually exclusive? Support your answer using the laws of probability c. Are the two events A, and M, statistically independent? Support your answer using the laws of probability d. Are the two events A, and M, collectively exhaustive? Support your answer using the laws of probability.

Explanation / Answer

a) P(A U M) = P(A) + P(M) - P(A M)

P(M) = 1 - 0.5 + 0.35 = 0.85

b) P(A M) is not equal to 0 meaning the events can happen at the same time, therefore the events are not mutually exclusive

c) Not independent as P(A M is not equal to P(A)*P(M)

d) Yes as the probability of at least one of the scholarship is 1(Maximum probability) and therefore the two events are collectively exhaustive

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