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Question

An unbiased coin is tossed n times. Let E1 be the event that both heads and tails are present in n tosses. Let E2 be the event that the coin shows up heads at most once in n tosses. The value of n for which E1 and E2 are independent is

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Solution

n(S)=2n
n(E1)=2n2
n(E2)=nC1+1=n+1n(E1E2)=n
P(E1E2)=P(E1)×P(E2)n2n=2n22n×n+12nn=3

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