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Question
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 ______.
Options
`4/5`
`1/2`
`1/5`
`2/5`
Solution
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 `underline(4/5)`.
Explanation:
Let E1 = the coin will show the head
E2 = The coin will show the head
P(E1) = P(E2) = `1/2`
E = A says heads are revealed
P(heads come up and A tells the truth)
= `P(E/E_1)`
= `4/5`
P(Tips come out and A is not telling the truth)
= `P(E/E_2)`
= `1/5`
Intended process = `(4/5 xx 1/2)/((4/5 xx 1/2) + (1/5 xx 1/2))`
= `4/4 + 1`
= `4/5`
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