Multiple choice

A coin is tossed $n$ times. If the probability of getting head $6$ times is equal to the probability of getting head 8 times then $n : =$

  1. $6$
  2. $8$
  3. $14$
  4. $10$
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C Correct answer
Explanation

In a binomial distribution, P(X=k) = P(X=n-k) implies k + (n-k) = n, but here we have P(X=6) = P(X=8). The property of binomial coefficients states that nCr = nC(n-r), so 6 + 8 = n, which gives n = 14.

AI explanation

According to the binomial distribution, the probability of 6 successes is nC6 times (1/2)^n, and the probability of 8 successes is nC8 times (1/2)^n. Equating the two probabilities gives nC6 equals nC8. Using the property of combinations that nCr equals nC(n-r), we have n - 6 equals 8. Solving this equation yields n equals 14.

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