Chapter 5.3, Problem 78E

a.

To determine

To Draw: a tree diagram that shows the sample space of the chance process.

Explanation of Solution

Given:

Total number of switches contain in one shipment is $10000$ .

And the number of bad switches is $1000$ .

Calculation:

There are two options, thus two branches are nedded at each knot:

The probability is the number of favourable outcomesdivided by the number of possible outcomes:

  

b.

To determine

To find: the probability that both switches are defective.

Answer to Problem 78E

  $P\left(\text{Bad and Bad}\right)=0.009991$

Explanation of Solution

Given:

Total number of switches contain in one shipment is $10000$ .

And the number of bad switches is $1000$ .

Calculation:

Multiplying the corresponding probabilities so that to find the probability that both switches are defective.

Therefore,

  $\begin{array}{l}P\left(\text{Bad and Bad}\right)=P\left(\text{Bad}\right)+P\left(\text{Bad after Bad}\right)\\ =\frac{1000}{10000}\times \frac{999}{9999}=\frac{999}{99990}=0.009991\end{array}$ .

Hence, the probability that both switches are defective is $P\left(\text{Bad and Bad}\right)=0.009991$ .