A bag holds three coins: a fair coin, a coin with a head on both sides, and a coin that shows a head with probability $\frac{1}{4}$. A coin is picked at random and tossed. What is the probability of a head?

Explanation

1. 01

   Each coin is picked with probability $\frac{1}{3}$, and the coins show a head with probabilities $\frac{1}{2}$, 1 and $\frac{1}{4}$.

2. 02

   $\frac{1}{3}\left(\frac{1}{2} + 1 + \frac{1}{4}\right) = \frac{1}{3} \times \frac{7}{4} = \frac{7}{12}$.