Chapter 6.1, Problem 4E

Refer to the chance experiment described in the previous exercise and the sample space for that experiment.

1. a. List the outcomes in each of the following events. Which of these events are simple events? (Hint: See Example 6.3.)
   1. i. the event that at least one car has an automatic transmission
   2. ii. the event that exactly one car has an automatic transmission
   3. iii. the event that neither car has an automatic transmission
2. b. What outcomes are in the event B and C? In the event B or C?

6.3 Consider the chance experiment in which the type of transmission—automatic (A) or manual (M)—is recorded for each of the next two cars purchased from a certain dealer.

1. a. What is the set of all possible outcomes (the sample space)? (Hint: See Example 6.2.)
2. b. Display the possible outcomes in a tree diagram.

Example 6.3 Turning Directions

A traffic engineer has been asked to consider whether a stop sign at the bottom of a freeway off-ramp should be replaced by a traffic light. To help in this decision, she plans to observe traffic patterns for this off-ramp. Suppose she were to record the turning direction (L = left or R = right) of each of three successive vehicles. This is a chance experiment and the sample space contains eight outcomes;

Each of these outcomes determines a simple event. Other events include

A = event that exactly one of the cars turns right = {RLL, LRL, LLR}

B = event that almost one of the cars turns right - {LLL, RLL, LRL. LLR}

C = event that all cars turn in the same direction = {LLL, RRR}

Some other events that can be formed from the events just defined are

$\begin{array}{l}notC=C^c\text{ = event that not all cars turn in the same direction}\\ =\text{{RLL, LRL, LLR, RRL, RLR, LRR}}\end{array}$

$\begin{array}{l}AorC=A\cup C\text{ = event that exactly one of the cars turns right or all cars turn in the same direction}\\ =\text{{RLL, LRL, LLR, LLL, RRR}}\end{array}$ $\begin{array}{l}B\text{ and }C\text{ = }B\cap C\text{ = event that at most one car turns right and all cars turn in the same direction}\\ =\text{{LLL}}\end{array}$