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Question

A speaks truth 3 times out of 4, and B speaks 7 times out of 10; they both assert that a white ball has been drawn from a bag containing 6 balls all of different colours. Find the probability of the truth of the assertion.

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Solution

There are two hypothesis; (i) their coincident testimony is true, (ii) it is false.
Here P1=16,P2=56;
p1=34×710,p2=125×14×310;
For in estimating p2 we msut take into account the chance that A and B will both select the white ball when it has not been drawn; this chance is 15×15 or 125.
Now the probabilities of the two hypotheses are as P1p1 to P2p2, and therefore as 35 to 1; thus the probability that the statement is true is 3536.

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