An unbiased coin is tossed n times. Let X denote the number of ti
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An unbiased coin is tossed n times. Let X denote the number of times the head occurs. If P(X = 4), P(X = 5) and P(X = 6) are in AP, then the values of n can be
A. 7 , 14
B. 10 , 14
C. 12 , 7
D. None of these
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Given:
P(X = 4) , P(X = 5) and P(X = 6) are in A.P
Hence,
P(X = 4) + P(X = 6) = 2× P(X = 5)
Analysis:
For an unbiased coin, P(Head) = P(Tail) = 1/2
nC4 (1/2)4(1/2)n-4 + nC6 (1/2)6(1/2)n-6 = 2× nC5 (1/2)5(1/2)n-5
nC4 (1/2)n + nC6 (1/2)n = 2× nC5 (1/2)n
nC4 + nC6 = 2× nC5
Only n = 7 and n = 14 satisfies the above equation.