75. There are two identical urns. The first contains 2 black and 3 white balls, the second - 2 black and 1 white ball. First, an urn is chosen at random, and then one ball is drawn at random from it. What is the probability that a white ball will be selected?
Solution. Let event $A$ consist in the extraction of a white ball from a randomly chosen urn, and $H_{1}$ and $H_{2}$ be the hypotheses that it belongs to the first or second urn, respectively. Then the probability $P\left(H_{1}\right)=$ $=P\left(H_{2}\right)=\frac{1}{2}$, the probability that a white ball belongs to the first urn, $P\left(A / H_{1}\right)=\frac{3}{5}$, and the probability that a white ball belongs to the second urn, $P\left(A / H_{z}\right)=\frac{1}{3}$. By the formula of total probability we get

$$
P(A)=P\left(A / H_{1}\right) P\left(H_{1}\right)+P\left(A / H_{2}\right) P\left(H_{2}\right)=\frac{3}{5} \cdot \frac{1}{2}+\frac{1}{3} \cdot \frac{1}{2}=\frac{3}{10}+\frac{1}{6}=\frac{7}{15}
$$