Chapter 10.2, Problem 13E

To determine

To calculate:

The probability value of both events $A$ and $B$

Answer to Problem 13E

The probability value of both events $A$ and $B$ is $0.3474$ .

Explanation of Solution

Given information:

Event $A$ : Selection of the first sock of white colored

Event $B$ : Selection of the second sock also of white colored

Calculation:

In the first draw, need to select the first socks of white colored from $12$ white and $8$ black shocks. So, the probability of event $A$ is calculated as:

  $\begin{array}{l}P\left(A\right)=\frac{12}{12+8}\\ P\left(A\right)=\frac{12}{20}\end{array}$

In the next draw, need to select the second socks of also white colored from $11$ white and $8$ black shocks. So, the probability of event $B$ is calculated as:

  $\begin{array}{l}P\left(B\right)=\frac{11}{11+8}\\ P\left(B\right)=\frac{11}{19}\end{array}$

Now, the probability of the both events is calculated as:

  $\begin{array}{l}P\left(A\cap B\right)=P\left(A\right)\times P\left(B\right)\\ P\left(A\cap B\right)=\frac{12}{20}\times \frac{11}{19}\\ P\left(A\cap B\right)=0.3474\end{array}$