While reviewing, in preparation for an exam, three students: Amy, Bob, and Chris
ID: 3311619 • Letter: W
Question
While reviewing, in preparation for an exam, three students: Amy, Bob, and Chris are sitting together. The probabilities that Amy, Bob, and Chris can solve a certain problem independently are 0.2+ respectively. DGC ,0.4, and 0.3 DGC+200 Fig. 2.2. Preparing for final exam a) Find the probability that the problem will be solved by at least one of them if they try independently. (b) In part (a), if the probabilities that Amy and Bob together can solve the problem is 0.45; that Amy and Chris can solve the problem is 0.65; that Bob and Chris can solve the problem is 0.35; and that all together can solve the problem is 0.26. What is the probability that the problem will be solved by at least one of them?Explanation / Answer
probability that Amy can solve problem =0.2+446/(446+200)=0.8904
therefore probabllity that at least one of them solve problem =1-P(none will solve problem)
=1-(1-0.8904)*(1-0.4)*(1-0.3) =0.9540
b)
probability thaqt problem will be solved by at least one of them =P(AUBUC)
=P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)+P(AnBnC) =0.8904+0.4+0.3-0.45-0.65-0.35+0.26=0.4004
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