Algebra

Probability

Medium

core

A man is known to speak truth 4 out of 5 times. A coin is tossed. He reports that a head appears. The probability that actually there was a head, is

4/5

3/5

1/5

2/5

✅ Correct Option: 1

Let $H$ be the event of an actual head, $P(H)=P(T)=\frac12$ , and $E$ that he reports a head.

$P(E)=\frac12\cdot\frac45+\frac12\cdot\frac15=\frac12$ .

By Bayes' theorem, $P(H/E)=\frac{(1/2)(4/5)}{1/2}=\frac45$ .

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Solution

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