Chapter 11.4, Problem 32PPSE

Solution

(a)

Whether the tree branches represent conditional probabilities.

The tree branches represent conditional probabilities.

Given:

The tree diagram is given.

Calculation:

The tree diagram is represented as:

  

Conditional probability is defined as the probability of occurring an event based on the occurrence of previous event.

Hence, the branches A and M shows the conditional probability.

Conclusion:

The branches A and M shows the conditional probability.

(b)

Whether the event of having a license and the event of being an adult is an independent event or not.

No, these are not an independent event.

Given:

The tree diagram is given.

Calculation:

Independent events are those events whose occurrence does not depend on other events. Hence, having a license and being an adult are dependent on each other therefore, these events are not an independent event.

Conclusion:

No, these are not an independent event.

(c)

The probability of each tree branches.

The probability is $0.3$

Given:

The tree diagram is given.

Calculation:

  $\begin{array}{l}P(L)=\frac{50}{100}\times \frac{40}{100}+\frac{50}{100}\times \frac{20}{100}\\ P(L)=\frac{20}{100}+\frac{10}{100}\\ P(L)=\frac{3}{10}\\ P(L)=0.3\end{array}$

Conclusion:

The probability is $0.3$