Question

A box contains 5 balls. One is numbered 1, three are numbered 2, and one is numbered 3. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the mean of the numbers on the balls

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c} Number\ of\ ball\ x & 1 & 2 & 3 \\ \hline Probability \,P(X=x) & 1/5 & 3/5 & 1/5 \\ \end{array}$$

$$\mu=E(X)=1(\dfrac{1}{5})+2(\dfrac{3}{5})+3(\dfrac{1}{5})=2$$

The mean of the numbers on the balls is 2.