Chapter 13, Problem 2E

To determine

To calculate: To find the probability that the car is red and has leather interior

Answer to Problem 2E

The probability that the car is red and has leather interioris $\frac{1}{12}$

Explanation of Solution

Given information: A car manufacturer offers two kinds of transmission: Standard or automatic; two different interiors: leather or cloth; and six different colors: black, red, white, gray, yellow or blue

Formula Used:

Probability is defined as the likelihood of an event.

Probability is calculated as

  $\mathrm{Probability}=\frac{Event}{Outcomes}$

Calculation:

Given that a car manufacturer offers two kinds of transmission: Standard or automatic; two different interiors: leather or cloth; and six different colors: black, red, white, gray, yellow or blue

Let an event is defined as choosing a car at random

Total number of possible outcomes $=2\times 2\times 6=24$

Possible outcomes that car is red and has leather interior

Transmission	Interior	Color
Standard	Leather	Red
Automatic	Leather	Red

Hence, number of possible outcomes $=2$

Thus, probability that the car is red and has leather interioris calculated as

  $\begin{array}{l}P=\frac{2}{24}\\ P=\frac{1}{12}\end{array}$

Conclusion:

Hence, the required probability is $\frac{1}{12}$

Correct option is J