What is the probability of getting exactly 2 heads in 3 coin flips?

Problem: What is the probability of getting exactly 2 heads in 3 coin flips, represented as $P(X = 2)$ for a binomial distribution?

Steps

1. Identify the parameters of the binomial distribution
   $$n = 3, p = 0.5, q = 0.5$$
2. Apply the binomial probability formula
   $$P(X = k) = \binom{n}{k} p^k q^{n-k}$$
3. Substitute the values for $k = 2$
   $$P(X = 2) = \binom{3}{2} (0.5)^2 (0.5)^{3-2}$$
4. Calculate the combination
   $$P(X = 2) = 3 \cdot (0.5)^2 \cdot (0.5)^1$$
5. Simplify the expression
   $$P(X = 2) = 3 \cdot 0.25 \cdot 0.5$$
6. Multiply to find the final fraction
   $$P(X = 2) = \frac{3}{8}$$