InterviewSolution
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InterviewSolution
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A fair coin is flipped n times. Let E be the event "a head is obtained on the first flip" and let `F_(k)` be the event "exactly k heads are obtained". Then the value of n/k for which E and `F_(k)` are independent is _____. |
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Answer» Correct Answer - 2 Here `P(E)=1/2and P(F_(k))=""^(n)C_(k).(1)/(2^(n))` Also, `P(EnnF_(k))=p` (exactly k heads are obtained and head obtained in first filp) `=1/2""^(n-1)C_(k-1)((1)/(2))^(n-1)` Events E and `f_(k)` are independent. Therefore, `P(EnnF_(k))=P(E).P(F_(k))` `or ""^(n-1)C_(k-1)xx(1)/(2^(n))=1/2xx""^(n)C_(k)(1)/(2^(n))` `or2xx""^(n-1)C_(k-1)=""^(n)C_(k)` `orn=2k` |
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