Get Exactly 2 Heads in 4 Coin Flips

Model guide

Why this probability model fits

This is a binomial probability problem because the flips are independent, each flip has the same probability of heads, and the question asks for an exact success count.

Setup: Each flip has the same probability p = 0.5 for heads, and one flip does not change the next one.

Replacement: Replacement is not the right idea here. Coin flips are repeated independent trials, not draws from a shrinking pool.

Independence: Independence matters because the binomial model assumes the probability of heads stays the same on every flip.

Worked solution

37.5%

The probability of exactly 2 successes is 37.5%.

1. Identify this as repeated independent trials with the same success probability.
2. Use P(X = k) = C(n, k)p^k(1-p)^(n-k).
3. Set n = 4, target successes = 2, and p = 0.5.
4. Evaluate the required binomial term for the requested success range.
5. The final probability is 3/8, which is 37.5%.