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 \(y\) denote the number of cars observed. What are possible \(y\) values? List five different outcomes and their associated \(y\) values.

Short answer

The possible values for \(y\) are positive integers starting from 1. Five different outcomes and their associated \(y\) values could be: 1) R, R, R, S with \(y = 4\); 2) L, L, S with \(y = 3\); 3) R, L, S with \(y = 3\); 4) R, S with \(y = 2\); 5) S with \(y = 1\).

Step-by-step solution

Understand the Problem

The problem talks about an experiment involving cars and their directions at an intersection. The cars could either go straight ahead (S), turn left (L), or turn right (R). According to the problem, the experiment ends as soon as a car goes straight. Therefore, it would be safe to say that the number of cars observed (\(y\)) is the number of turns before a straight occurs. That number can't be zero because at least one car (the one that goes straight) is observed.

Identify Possible Y Values and Outcome

Given the problem, the possible \(y\) values are positive integers starting from 1. This is because at least one car (the one that goes straight) is observed, so \(y\) can't be zero. We start listing the complicated outcomes first. For example, a car might turn right, then another turn right again, then another goes straight, giving \(y = 3\). Similarly, a car might turn left, then the next one goes straight, giving \(y = 2\). If the first car goes straight, then \(y = 1\).

Listing Different Outcomes and Their Y values

We now list five different outcomes and their associated \(y\) values. Note that, for each scenario, 'S' must be the last turn since it ends the experiment. 1. Scenario: R, R, R, S. Here, \(y = 4\). 2. Scenario: L, L, S. Here, \(y = 3\), 3. Scenario: R, L, S. Here, \(y = 3\), 4. Scenario: R, S. Here, \(y = 2\), 5. Scenario: S. Here, \(y = 1\). These different scenarios and corresponding \(y\) values explain the nature of the experiment.