Q.

A bag contains  2n+1 coins. It is known that n of these coins have a head on both sides where as the rest of the coins are fair. A coin is picked up at random form the bag and is tossed. If the probability that the results in a head is 3142, then the value of n is

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a

7

b

10

c

12

d

8

answer is B.

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Detailed Solution

Given, n coins have head on both sides and (n+1) coins are fair coins.  Let E1= Event that an unfair coin is selected E2= Event that a fair coin is selected H= Event that the toss result in a head P(H)=PE1⋅PH/E1+PE2⋅PH/E23142=n2n+1⋅1+n+12n+1⋅12 ⇒ n=10
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