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

Question

3. 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 0.15. The probability of getting at least one of the scholarships is 0.3. Show your work, NOT just answers.

(1) What is the probability that you will receive a Merit scholarship?

(2) What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?

Explanation / Answer

P(athletic scholarship) = 0.18

P(both scholarship) = 0.15

P(at least one scholarship) = 0.3

1) P(at least one scholarship) = P(Athletic scholarship) + P(Merit scholarship) - P(both scholarship)

Or, 0.3 = 0.18 + P(Merit scholarship) - 0.15

Or, P(Merit scholarship) = 0.27

B) P(Athletic scholarship | Merit scholarship) = P(both scholarship) / P(Merit scholarship)

= 0.15 / 0.27

= 0.5556

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