$X$ takes the values 1, 2 and 3 with probabilities 0.2, $p$ and $0.8 - p$. If $E(X) = 2.2$, what is $p$?

Explanation

1. 01

   $E(X) = 0.2 + 2p + 3(0.8 - p) = 2.6 - p$.

2. 02

   $2.6 - p = 2.2$, so $p = 0.4$ (and $P(X = 3) = 0.4$).