Multiple choice

A fair coin is tossed n times. if the probability that head occurs $6$ times is equal to the probability that head occurs $8$ times, then value of $n$ is

  1. $24$
  2. $48$
  3. $14$
  4. $16$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For binomial probability P(X=k) = C(n, k) * p^k * (1-p)^(n-k). Since p=0.5, P(X=6) = P(X=8) implies C(n, 6) = C(n, 8). Thus 6 + 8 = n, so n = 14.

AI explanation

Using the binomial probability formula, the probability of getting exactly k heads in n tosses is given by the combination of n choose k multiplied by (1/2)^n. The condition states that the probability of 6 heads equals the probability of 8 heads, meaning n choose 6 equals n choose 8. By the symmetry property of combinations, if n choose r equals n choose s, then r plus s equals n, so 6 plus 8 equals 14, making the value of n equal to 14.

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