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Probability that A speaks truth is 4/5. A coin is tossed. A reports that a head appears. The probability that actually there was head is

Given: let E_{1} be the event that A speaks truth, E_{2} be the event that A lies and X be the event that it appears head.

Therefore,

As E_{1} and E_{2} are the events which are complimentary to each other.

Then P (E_{1}) + P (E_{2}) = 1

⇒ P (E_{2}) = 1 - P (E_{1})

⇒ P (E_{2})

If a coin is tossed it may show head or tail.

Hence the probability of getting head is 1/2 whether A speaks a truth or A lies.

P(X|E_{1}) = P(X|E_{2}) = 1/2

Now the probability that actually there was head, give that A speaks a truth is P(E_{1}|X).

By using bayes’ theorem, we have:

Therefore correct answer is (A).

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If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is correct?

(view answer)