Three Heads in Four Flips

Count how many of the $16$ equally likely flip sequences contain exactly three heads.

Use the binomial coefficient $\left(\genfrac{}{}{0ex}{}{4}{3}\right)$ to count the favorable sequences.

1. 1. Count favorable outcomes

   There are $\left(\genfrac{}{}{0ex}{}{4}{3}\right)=4$ ways to choose which three flips land heads.

   $$\left(\genfrac{}{}{0ex}{}{4}{3}\right)=4$$

2. 2. Divide by the sample space

   There are $2^4=16$ equally likely sequences of four flips.

   $$P=\frac{4}{16}=\frac{1}{4}$$

Answer: 1/4