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Question

A bag contains (2n+1) coins. It is known that n of these coins have a head on both sides, whereas the remaining (n+1) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is 3142, then n is equal to

A
10
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B
11
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C
12
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D
13
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Solution

The correct option is A 10
E1: biased coin is chosen,
E2: fair coin is choice.
and A: toss results in a head.
P(E1)=n/(2n+1),P(E2)=(n+1)/(2n+1)
P(A|E1)=1 and P(A|E2)=1/2
By the total probability rule
3142=n2n+1(1)+(n+1)2(2n+1)3n+12n+1=3121n=10

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