In n independent coin flips with probability 0.5 of heads, the number of heads follows which distribution?

• A. Poisson(0.5)
• B. Binomial(n, 0.5)
• C. Normal(n, 0.5)
• D. Geometric(n, 0.5)

Answer: (B)

This question tests how many successes you expect when you fix the number of trials and each trial has the same chance of success. Flipping a coin n times, the number of heads is the sum of n independent Bernoulli(0.5) trials, which follows a binomial distribution with parameters n and p = 0.5. So the exact distribution is Binomial(n, 0.5).

The probability of getting exactly k heads is C(n, k) (0.5)^k (0.5)^(n-k) = C(n, k) 2^-n, with mean np = n/2 and variance np(1-p) = n/4.

Other distributions don’t fit this setup: Poisson would require a different modeling scenario (rare events with rate lambda = np, not a fixed n with p fixed); Normal would be a continuous approximation and, if used, would have parameters np and sqrt(np(1-p)) for the appropriate approximation; Geometric counts trials until the first success, not the total number of successes in a fixed number of trials.