6· 018 points l Previous Answers My Notes Ask Your Teach Sam and Allen have appl

Question

6· 018 points l Previous Answers My Notes Ask Your Teach Sam and Allen have applied for scholarships. The probability that Sam gets a scholarship is 0.88. The probability that Allen gets a scholarship is 0.76. The probability they both get scholarships is 0.73 (a) What is the probability that Sam gets a scholarship but Allen doesn't? 0.21 (b) What is the probability neither receives a scholarship? 0.27 (c) If Sam receives a scholarship, what then is the conditional probability that Allen will also receive a scholarship? (d) If Allen receives a scholarship, what then is the conditional probability that Sam will not receive a scholarship? 0.12

Explanation / Answer

Sam gets scholarship: A

Allen gets scholarship: B

P(A)=0.88, P(B)=0.76 and P(A and B)=0.73

P(A or B)=P(A)+P(B)-P(A and B)=0.88+0.76-0.73=0.91

a) P(A and not B)=P(A)-P(A and B)=0.88-0.73=0.14

b) P(neither)=1-P(A or B)=1-0.91 =0.09

c) P(B|A)=P(A and B)/P(A)=0.73/0.88 =0.8295

d) P(not A|B)=P(not A and B)/P(B)=(P(B)-P(A and B))/P(B)=(0.76-0.73)/0.76 =0.03947

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