This website uses cookies to ensure you get the best experience on our website.
By using this site, you agree to our Privacy Policy.
Question Directory
Two Drawers
There are two drawers. One contains only black balls, and the other contains 50% white balls and 50% black balls. You pick a drawer at random and select a ball. What is the probability that it is white?
Let us denote the event of selecting a white ball as $W$ and the events of opening drawer 1 and drawer 2 as $D_1$ and $D_2$ respectively. By the law of total probability we have
$$
P(W) = P(W | D_1) P(D_1) + P(W | D_2) P(D_2).
$$
Given that we select a drawer at random,
$$
P(D_1) = P(D_2) = 0.5.
$$
As drawer 1 only contains black balls we have
$$
P(W | D_1) = 0
$$
and for drawer 2, as there are 50% white balls and 50% black balls we have
$$
P(W | D_2) = 0.5.
$$
Plugging these values in we find that
$$
P(W) = 0.5 \times 0.5 = 0.25.
$$