Chapter 11.9, Problem 13E

a.

To determine

To find the probability of choosing 2 blue socks.

Answer to Problem 13E

The probability of choosing 2 blue socks is $\frac{2}{51}$ .

Explanation of Solution

Given information:

A drawer contains 4 blue socks, 6 gray socks, and 8 black socks.

Calculation:

Let P be the probability of choosing 2 blue socks.

Total number of blue socks is 4.

Total number of socks $=4+6+8=18$

Therefore,

Probability of choosing blue socks in first selection is $\frac{4}{18}$ .

Probability of choosing blue socks in second selection is $\frac{3}{17}$ .

Probability of choosing 2 blue socks is $\frac{4}{18}\times \frac{3}{17}=\frac{2}{51}$

Hence,

The probability of choosing 2 blue socks is $\frac{2}{51}$ .

b.

To determine

To find the probability of choosing 2 blue socks.

Answer to Problem 13E

The probability of choosing 2 gray socks is $\frac{5}{51}$ .

Explanation of Solution

Given information:

A drawer contains 4 blue socks, 6 gray socks, and 8 black socks.

Calculation:

Let P be the probability of choosing 2 blue socks.

Total number of gray socks is 6.

Total number of socks $=4+6+8=18$

Therefore,

Probability of choosing gray socks in first selection is $\frac{6}{18}$ .

Probability of choosing gray socks in second selection is $\frac{5}{17}$ .

Probability of choosing 2 blue socks is $\frac{6}{18}\times \frac{5}{17}=\frac{5}{51}$

Hence,

The probability of choosing 2 gray socks is $\frac{5}{51}$ .

c.

To determine

To find the probability of choosing 2 black socks.

Answer to Problem 13E

The probability of choosing 2 black socks is $\frac{2}{51}$ .

Explanation of Solution

Given information:

A drawer contains 4 blue socks, 6 gray socks, and 8 black socks.

Calculation:

Let P be the probability of choosing 2 black socks.

Total number of black socks is 8.

Total number of socks $=4+6+8=18$

Therefore,

Probability of choosing black socks in first selection is

  $\frac{8}{18}$ .

Probability of choosing black socks in second selection is $\frac{7}{17}$ .

Probability of choosing 2 black socks is

  $\frac{8}{18}\times \frac{7}{17}=\frac{28}{153}$

Hence,

The probability of choosing 2 black socks is $\frac{28}{153}$ .

d.

To determine

To find the probability of choosing same color socks.

Answer to Problem 13E

The probability of choosing same color socksis

  $\frac{49}{153}$ .

Explanation of Solution

Given information:

A drawer contains 4 blue socks, 6 gray socks, and 8 black socks.

Calculation:

Let P be the probability of choosing same color socks.

The probability of choosing 2 blue socks is $\frac{2}{51}$ .

The probability of choosing 2 gray socks is

  $\frac{5}{51}$ .

The probability of choosing 2 black socks is $\frac{28}{153}$ .

Hence,

The probability of choosing same color socks is $\frac{2}{51}+\frac{5}{51}+\frac{28}{153}=\frac{6+15+28}{153}=\frac{49}{153}$ .