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
- A \(7\)
- B \(14\)
- C \(21\)
- D \(28\)
Answer & Solution
Correct Answer
(B) \(14\)
Step-by-step Solution
Detailed explanation
\(2 P(X=5) = P(X=4) + P(X=6)\) \(2 \binom{n}{5} (0.5)^n = \binom{n}{4} (0.5)^n + \binom{n}{6} (0.5)^n\) \(2 \binom{n}{5} = \binom{n}{4} + \binom{n}{6}\) \(2 \frac{n!}{5!(n-5)!} = \frac{n!}{4!(n-4)!} + \frac{n!}{6!(n-6)!}\)…
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