A speaks truth only when B does not speak truth then what is the probability that C does not speak t...........

Quantitative Aptitude ( CCS) Probability

Directions : There are 3 people – A, B and C. Probability that A speaks truth is 3/10, probability that B speaks truth is 3/7 and probability that C speaks truth is 5/6. For a particular question asked, at most 2 people speak truth. All people answer to a particular question asked.

A speaks truth only when B does not speak truth, then what is the probability that C does not speak truth on a question?

11/140

21/180

22/170

13/140

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Explanation:

Case 1: B does not speak truth, A speaks truth
So A speaks truth here
Probability that C does not speak truth = 3/10 * (1 – 3/7) * ( 1- 5/6) = 1/35
Case 2: B speaks truth
So A does not speak truth here
Probability that C does not speak truth = ( 1- 3/10) * 3/7 * ( 1- 5/6) = 1/20
So total = 1/35 + 1/20 = 11/140

Hence, option 1 is the correct answer.