11. Assume you have applied for two scholarships, a Merit scholarship (M) and an

Question

11. 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 O.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3. Briefly discuss your results. a. b. c. d. What is the probability that you will receive a merit scholarship? Are events A and M mutually exclusive? Why or why not? Explain. Are the two events A and M independent? Explain using probabilities. What is the probability of receiving the athletic scholarship given that you have been awarded the merit scholarship? What is the probability of receiving the merit scholarship given that you have been awarded the athletic scholarship? Briefly discuss.

Explanation / Answer

here M=merit scholarship and A=athletic scholarship

P(A)=0.18 , P(A and M)=0.11, P(A or M)=0.3

(a) answer P(M)=0.23

we know that P(A or M)=P(A)+P(M)-P(A and M)

P(M)=P(A or M)+P(A and M)-P(A)=0.3+0.11-0.18=0.23

(b)for A and M would be mutually exclusive if P(A and M)=0

so A amd M is not mutually exclusive as P(A and M)=0.11

(c)P(A)*P(M)=0.23*0.18=0.414 which is not equal to P(A and M)=0.11

so A and M are not indpendent

for independence of A and M there should be P(A and M)=P(A)*P(M)

(d)required probability=P(A|M)=P(A and M)/P(M)=0.11/0.23=0.4783

(e)required probability =P(M|A)=P(M and A)/P(A)=0.11/0.18=0.6111

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