A man is known to speak the truth 5 out of 7 times. He throws a die and a number other than six comes up. Find the probability that he reports it is a six.

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\frac{2}{7}

\frac{3}{7}

\frac{4}{7}

\frac{5}{7}

answer is A.

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Detailed Solution

Given that, a man is known to speak the truth 5 out of 7 times.
The P(A) of the random experiment as,

P (A) = \frac{Number of favorable outcomes}{Total number of outcomes}

He throws a die and a number other than six comes up and if he reports it as 6, then that means he is lying.
The probability that he speaks truth is given as,

P = \frac{5}{7}

.
Since the number of times, he does not speak the truth is 2.
Therefore, the probability that he is lying is,

\underset{̲}{P} = \frac{2}{7}

The probability is

\frac{2}{7}

.
Hence, option 1 is the correct answer.

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