Question

Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead (S). The experiment terminates as soon as a car is observed to go straight. Let \(x\) denote the number of cars observed. What are possible \(x\) values? List five different outcomes and their associated \(x\) values. (Hint: See Example 6.2)

Short answer

The possible \( x \) values are 3, 2, 3, 4, and 1 for the outcomes \( LRS \), \( RS \), \( LLS \), \( RLRS \), and \( S \), respectively.

Step-by-step solution

Understanding the experiment process

In the intersection, each passing car has 3 options: it can either turn right (R), turn left (L), or go straight (S). We start to count the number of cars when the observation begins and stop counting when we see a car going straight.

Define possible outcomes

An outcome is observed when a car goes straight, ending the experiment. Prior to this, the car could have either turned left or right. Consequently, the possible outcomes will be sequences of L and/or R followed by S. For example, \( LRS \), \( RS \), \( LLS \), \( RLRS \}, and \( S \) are all possible outcomes.

Corresponding x values

The value of \( x \) is equivalent to the number of cars observed during each of these outcomes. For \( LRS \), \( x = 3 \); for \( RS \), \( x = 2 \); for \( LLS \), \( x = 3 \); for \( RLRS \), \( x = 4 \); and for \( S \) alone, \( x = 1 \).