Q. 164.7( 3 Votes )

A, B, and C are independent witness of an event which is known to have occurred. A speaks the truth three times out of four, B four times out of five and C five times out of six. What is the probability that the occurrence will be reported truthfully by majority of three witnesses?

Answer :


A speaks truth three times out of four

B speaks truth four times out of five

C speaks truth five times out of six

P(TA) = P(A speaks truth)

P(TB) = P(B speaks truth)

P(TC) = P(C speaks truth)

P(NA) = P(A speaks lies)

P(NB) = P(B speaks lies)

P(NC) = P(C speaks lies)


It is told that the occurrence is will be reported by majority of witness. This is only possible when at least two of the witnesses speaks truth.


Since speaking by a person is independent the probabilities will multiply each other.

P(M) = (P(TA)P(TB)P(NC)) + (P(TA)P(NB)P(TC)) + (P(NA)P(TB)P(Tc)) + (P(TA)P(TB)P(TC))


The required probability is .

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