Two Heads in Three Flips

Count all equally likely outcomes of three flips.

Use the binomial formula $\left(\genfrac{}{}{0ex}{}{3}{2}\right)p^2(1-p)$ with $p=1/2$.

1. 1. Set up sample space

   There are $2^3=8$ equally likely outcomes.

2. 2. Count favorable outcomes

   The number of ways to choose which 2 of 3 flips are heads is $\left(\genfrac{}{}{0ex}{}{3}{2}\right)=3$.

   $$\left(\genfrac{}{}{0ex}{}{3}{2}\right)=3$$

3. 3. Compute probability

   Probability is favorable over total.

   $$P=\frac{3}{8}$$

Answer: 3/8