Chapter PIV, Problem 37RE

(a)

To determine

To find: the probability that end up wearing two blue socks.

Answer to Problem 37RE

0.0909

Explanation of Solution

The chance of a blue sock being drawn is $\frac{4}{12}$ .

If 2 socks are caught at random, it will be likely to draw 2 blue socks,

  $\left(\frac{4}{12}\right)\left(\frac{3}{11}\right)=0.0909$

(b)

To determine

To find: the probability that end up wearing no grey socks.

Answer to Problem 37RE

0.31818

Explanation of Solution

The chance of a non-grey sock drawing is $\frac{7}{12}$ .

The chance that 2 non-grey socks are drawn is,

  $\left(\frac{7}{12}\right)\left(\frac{6}{11}\right)=0.31818$

(c)

To determine

To find: the probability that end up wearing minimum one black sock.

Answer to Problem 37RE

0.4545

Explanation of Solution

Probability of at least 1 black sock drawing

  $\begin{array}{c}=1-\text{probability of drawing no black sock}\\ \text{=}1-\left(\left(\frac{9}{12}\right)\left(\frac{8}{12}\right)\right)\\ =1-0.5454\\ =0.4545\end{array}$

(d)

To determine

To find: the probability that end up wearing a green sock.

Answer to Problem 37RE

Zero

Explanation of Solution

The chance of a sock drawing is 0.

(e)

To determine

To find: the probability that end up wearing matching socks.

Answer to Problem 37RE

0.2878

Explanation of Solution

The probability that matching socks are drawn is,

  $\begin{array}{c}P\left(\text{two blue}\right)+P\left(\text{two}\text{grey}\right)+P\left(\text{two black}\right)\\ =\left(\frac{4}{12}\right)\left(\frac{3}{11}\right)+\left(\frac{5}{12}\right)\left(\frac{4}{11}\right)+\left(\frac{3}{12}\right)\left(\frac{2}{11}\right)\\ =0.0909+0.1515+0.04545\\ =0.2878\end{array}$