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MathematicsMathematics
29 December, 14:57

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?

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Answers (1)
  1. 29 December, 15:00
    0
    Step-by-step explanation:

    Given that 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

    P (A) = 0.18

    The probability of receiving both scholarships is 0.11.

    P (AM) = 0.11

    The probability of getting at least one of the scholarships is 0.3.

    P (AUM) = 0.3

    i. e. P (AUM) = P (A) + P (M) - P (AM) = 0.3

    0.18+P (M) - 0.11 = 0.3

    P (M) = 0.41-0.18 = 0.23

    a) the probability that you will receive a Merit scholarship=0.23

    b) P (AB) not equals 0

    Hence A and B are not mutually exclusive

    c) P (AM) = 0.11 and P (A) * P (M) = 0.23*0.18 not equals 0.11

    Hence not independent

    d) P (A/M) = P (AM) / P (M) = 0.11/0.23 = 0.4783
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