Chapter CSB, Problem 4.2E

To determine

Find the probability that he will first select blue sock, then a black sock and then another blue sock.

Answer to Problem 4.2E

  $\frac{5}{204}.$

Explanation of Solution

Given information:

Mr. $Y$ has $4$ black socks, $6$ blue socks and $8$ white socks in his drawer.

He selects $3$ socks at random without replacement.

Calculation:

The total number of socks in the drawer is $4+6+8=18$

As there are $6$ blue socks, the probability that he will first select blue sock is $\frac{6}{18}.$

Since, there is no sock replaced, the number of socks remained is $17.$

In the second drawing, as there are $4$ black socks, the probability that he will select black sock is $\frac{4}{17}.$

In the third drawing, as there are $5$ blue socks, the probability that he will select blue sock is $\frac{5}{16}.$

As, the three events are independent, the probability that he will first select blue sock, then a black sock and then another blue sock is,

  $\frac{6}{18}\times \frac{4}{17}\times \frac{5}{16}=\frac{5}{204}$

Hence, the probability that he will first select blue sock, then a black sock and then another blue sock is $\frac{5}{204}.$