Multiple choice

The probability of obtaining $2$ heads when an unbiased coin is tossed $5$ times is

  1. $\displaystyle \frac{5}{8}$
  2. $\displaystyle \frac{4}{9}$
  3. $\displaystyle \frac{5}{16}$
  4. $\displaystyle \frac{4}{16}$
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C Correct answer
Explanation

Using the binomial probability formula P(X=k) = C(n, k) * p^k * q^(n-k). Here n=5, k=2, p=0.5, q=0.5. Probability = C(5, 2) * (0.5)^2 * (0.5)^3 = 10 * (0.5)^5 = 10 / 32 = 5 / 16.

AI explanation

This uses the binomial probability formula, where the probability of exactly k successes in n trials is nCk * p^k * q^(n-k). Here, n = 5, k = 2, p = 1/2, and q = 1/2. The calculation is 5C2 * (1/2)^2 * (1/2)^3 = 10 * (1/32) = 10/32, which simplifies to 5/16.

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