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The odds that a Ph.D. thesis will be favourably reviewed by three independent examiners are 5 to 2, 4 to 3, and 3 to 4 respectively. What is the probability that: of the three examiners: (a) all reject the thesis, (b) all approve the thesis, (c) a majority approve the thesis.
P(X) be the probability that X reviews the thesis favourably.
P(A) = 5/7
P(B) = 4/7
P(C) = 3/7
Probability that all reject the thesis = (1-P(A)(1-P(B))(1-P(C)) = 2/7*3/7*4/7 = 24/343
Probability that all approve the thesis = P(A).P(B).P(C) = 5/7*4/7*3/7 = 60/343
Majority approve the thesis = P(A).P(B).(1-P(C)) + P(B).P(C).(1-P(A)) + P(A).P(C).(1-P(B)) [Two approve one reject]
= 5*4*4/343 + 4*3*2/343 + 5*3*3/343 = (80+24+45)/343 = 149/343
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