25-42 ■ Probability These exercises involve probability.

Choosing Socks A drawer contains an unorganized collection of 50 socks; 20 are red and 30 are blue. Suppose the lights go out, so Kathy can't distinguish the color of the socks.

(a).What is the minimum number of socks Kathy must take out of the drawer to be sure of getting a matching pair?

(b) If two socks are taken at random from the drawer, what is the probability that they make a matching pair?

(a)

To find:

The minimum number of socks Kathy must take out of the drawer to be sure of getting a matching pair.

Given:

A drawer contains an unorganized collection of 50 socks; 20 are red and 30 are blue.

Approach:

The first selected sock can be either red or blue. There are two possibilities of choosing second socks, that is, it can be either red or blue. Thus, it is not sure that the pair will be a matching pair. But on choosing the third sock, it is sure that it will be a matching pair because it will match either with the first sock or the second sock

(b)

To find:

The probability that they make a matching pair if two socks are taken at random from the drawer.