Chapter 8, Problem 75CR

To determine

To find: the probability to get a matched pair.

Answer to Problem 75CR

The probability to get a match pair = $\frac{1}{9}$ .

Explanation of Solution

Given information: Given five pairs of socks (no two pairs are the same color) to

randomly select two socks from a drawer.

Formula used:

Formula for the number of combinations of n numbers taken r numbers at a time is,

  $n(S){=}_n{C}_r.$

If an event has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, then the probability of event is given by,

  $P(E)=\frac{n(E)}{n(S)}.$

Calculation:

There are 10 socks and to choosing 2 from 10, the number of possible combination is,

  $n(S){=}_n{C}_r{=}_{10}{C}_2=\frac{10\times 9}{2\times 1}=45.$

Possible pairs of socks are 5 pairs.

So,

n (E) =5.

So,

  $P(E)=\frac{n(E)}{n(S)}=\frac{5}{45}=\frac{1}{9}.$