Suppose Pr(A wins at Melbourne) = Pr(A wins M) = 0.6, Pr(B wins at Roland Garros) = Pr(B wins RG) = 0.7, and suppose that these are independent events.
Suppose now that Pr(C wins at Wimbledon) = Pr(C wins W) depends upon these events, as C has just returned from injury.
Let Pr(C wins W | A wins M, B wins RG) = a, Pr(CwinsW |AwinsM,Bdoesn’twinRG)=b, Pr(CwinsW |Adoesn’twinM,BwinsRG)=c, Pr(CwinsW |Adoesn’twinM,Bdoesn’twinRG)=d.
1a) In terms of a, b, c and d, what is the probability that C wins W?
A well-known confidential sports predictor thinks that a = d = 0.25 and b = c = 0.8. 1b) If these beliefs were true, then what would be the probability that C wins W? For both 1a) and 1b), show your working.
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