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

Approved