Say the samples are as follows:
\(w_1\)={A,A}, \(w_2\)={A,B}, \(w_3\)={A,C},
\(w_4\)={B,A}, \(w_5\)={B,B}, \(w_6\)={B,C},
\(w_7\)={C,A}, \(w_8\)={C,B}, \(w_9\)={C,C}
And the first grade is John’s, and the second is Mary’s.
We are given that:
probability of John getting a B
P(\(w_4\)) + P(\(w_5\)) + P(\(w_6\)) = .3
probability of Mary getting a B
P(\(w_2\)) + P(\(w_5\)) + P(\(w_8\)) = .4
probability that neither gets an A but at least one gets a B
P(\(w_5\)) + P(\(w_6\)) + P(\(w_8\)) = .1
Adding the first two equations and subtracting the third equation, we get the probability that at least one gets a B but neither gets a C.
P(\(w_2\)) + P(\(w_4\)) + P(\(w_5\)) = .6