and an Athletic 4. Assume you have applied for two scholarships, a Merit scholar
ID: 3365653 • Letter: A
Question
and an Athletic 4. Assume you have applied for two scholarships, a Merit scholarship (M) scholarship (A). The probability that you will receive an Athletic scholarship is 0.50. The probability of receiving both scholarships is 0.35. The probability of getting at least one is 1.00. [12 points] a. What is the probability that you receive a Merit 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) probability of getting a Merit scholarship =P(M)=P(AUM)+P(AnM)-P(A)=1+0.35-0.5=0.85
b) No as P(AnM)= 0.35 which is not equal to 0 ; tehrefore they are not mutually exclusive
c)
No as P(A)*P(M) =0.85*0.5=.425 which is not equal to P(AnM) ; therefore A and M are not statistically independent.
d)
Yes as P(AUM)=1 ; therefore at least on of the events must happen; hence collectively exhaustive
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