chapter 5

A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year?

• (A) Less than 0.01

• (B) 0.078

• (C) 0.080

• (D) 0.922

• (E) Greater than 0.99

The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. The probability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?

• 0.05

• 0.06

• 0.10

• 0.40

• 0.50

In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course?

• 0.45

• 0.32

• 0.20

• 0.13

• 0.05

Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6 ?

The distribution of colors of candies in a bag is as follows.

If two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color?

• 0.09

• 0.22

• 0.25

• 0.75

• 0.78

A sample of 942 homeowners are classified, in the two-way frequency table below, by the number of credit cards they have and the number of years they have owned their current homes.

Of the homeowners in the sample who have four or more credit cards, what proportion have owned their current homes for at least one year?