Chapter 15, Problem 33E

(a)

To determine

To Explain: that the first flight is leaving on time and the luggage making the connection independent events.

Explanation of Solution

Given:

  $\begin{array}{c}P\left(F\right)=0.15\\ P\left(L|F\right)=0.95\\ P\left(L|F\text{'}\right)=0.65\\ P\left(F\text{'}\right)=1-0.15\\ =0.85\end{array}$

Calculation:

F= First fight is on time

L = Luggage will make the connection flight

  

By seeing the diagram it is clear that, the probability that the luggage arrives on time depends on whether the flight is on time. There is 95% probability when the Flight is on- time and only 65% when not.

(b)

To determine

To find: the probability that her luggage arrives in Denver with her.

Answer to Problem 33E

0.695

Explanation of Solution

Given:

  $\begin{array}{c}P\left(F\right)=0.15\\ P\left(L|F\right)=0.95\\ P\left(L|F\text{'}\right)=0.65\\ P\left(F\text{'}\right)=1-0.15\\ =0.85\end{array}$

Calculation:

Computer the probability that her luggage arrives in Denver with her

  $\begin{array}{c}P=\left(0.15\times 0.95\right)+\left(0.85\times 0.65\right)\\ =0.1425+0.5525\\ =0.695\end{array}$

Thus, the probability that her luggage arrives in Denver with her is 0.695 or 69.5%