A man is known to speak truth 3 out of 4 times. Find the probability that he lies.

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34

14

12

1

answer is B.

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Detailed Solution

It is given that a man speaks truth 3 out of 4 times. He throws a die and a number other than six comes up.
For an event E and not getting E, sum of probabilities is 1.

P (E) + P (E ¯) = 1

Therefore, the probability that a man speaks the truth is

\frac{3}{4}

.
Let

E

be an event that he speaks truth.
So,

E ¯

is the event that he lies.
Therefore, its probability is,

P (E) + P (E ¯) = 1 ⇒ 34 + P (E ¯) = 1 ⇒ P (E ¯) = 1 − 34 ⇒ P (E ¯) = 14

Thus, the probability that he lies is

14

.
So, the correct option is 2.

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