Chapter PIV, Problem 6RE

(a)

To determine

To find: the percentage of these employees with either hand cannot control the switch.

Answer to Problem 6RE

3%

Explanation of Solution

Given:

  $\begin{array}{c}\text{P}\left(\text{A}\right)=0.66\\ \text{P}\left(\text{B}\right)=0.82\\ \text{P}\left(\text{A}\cap \text{B}\right)=0.51\end{array}$

Formula used:

  $\text{P}\left(\text{A}\cup \text{B}\right)\text{=P}\left(\text{A}\right)\text{+P}\left(\text{B}\right)\text{-P}\left(\text{A}\cap \text{B}\right)$

Calculation:

Let

A = If employees had been successful with their left hands

B = If employees had been successful with their right hands

  $\text{A}\cap \text{B}$ = If employees had been successful with their both hands

So there have to found $1-\left(\text{A}\cup \text{B}\right)$

  $\begin{array}{c}\text{P}\left(\text{A}\cup \text{B}\right)\text{=P}\left(\text{A}\right)\text{+P}\left(\text{B}\right)\text{-P}\left(\text{A}\cap \text{B}\right)\\ =0.66+0.82-0.51\\ =0.97\end{array}$

The percentage of employees who have not been able to operate the switch with either hand is $\begin{array}{c}1-\left(\text{A}\cup \text{B}\right)\\ =1-0.97\\ =0.03\%\\ =3\%\end{array}$

(b)

To determine

To Explain: the success of independent events with the left and right hands.

Explanation of Solution

Since the occurrence of one event does not influence the occurrence of another event, performance with the right and left hands are different events.

(c)

To determine

To Explain: the success of mutually exclusive events with the left and right hands.

Explanation of Solution

Performance with right and left hands is not an occurrence that is mutually exclusive, as both events will occur at the same time.

More specifically, it can assume that events that are mutually exclusive are not independent and that events that are independent cannot be mutually exclusive.