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AP EAMCET · Maths · Probability

X denotes the number of times heads that occur in n tosses of a fair coin. If \(P(X=4), P(X=5)\) and \(P(X=6)\) are in arithmetic progression, the largest value of n is

  1. A \(7\)
  2. B \(14\)
  3. C \(21\)
  4. D \(28\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(14\)

Step-by-step Solution

Detailed explanation

\(2 P(X=5) = P(X=4) + P(X=6)\) \(2 \binom{n}{5} (0.5)^n = \binom{n}{4} (0.5)^n + \binom{n}{6} (0.5)^n\) \(2 \binom{n}{5} = \binom{n}{4} + \binom{n}{6}\) \(2 \frac{n!}{5!(n-5)!} = \frac{n!}{4!(n-4)!} + \frac{n!}{6!(n-6)!}\)…