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प्रश्न
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 ______.
विकल्प
`4/5`
`1/2`
`1/5`
`2/5`
उत्तर
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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Solution: Let A, C and T be the events that Mr. X goes to office by Auto, Car and Train respectively. Let L be event that he is late.
Given that P(A) = `square`, P(C) = `square`
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P(L) = P(A ∩ L) + P(C ∩ L) + P(T ∩ L)
`="P"("A")*"P"("L"//"A") + "P"("C")*"P"("L"//"C") + "P"("T")*"P"("L"//"T")`
`= square * square + square * square + square * square`
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`= square`
`"P"("C"//"L") = ("P"("L" ∩ "C"))/("P"("L"))`
= `("P"("C") * "P"("L"//"C"))/("P"("L"))`
`= (square * square)/square`
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| CASE-BASED/DATA-BASED |
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