Probability and Their Components

The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 am, what is the probability that the student will arrive at the college campus later than 9 am?

• 0.16

• 0.32

• 0.50

• 0.84

• 1.00

A complex electronic device contains three components, A, B, C. The probabilities of failure for each component in one year are 0.01, 0.03, 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?

• Less than 0.01

• 0.078

• 0.080

• 0.922

• Greater than 0.99

Joe and Matthew plan to visit a bookstore. Based on their previous visits to this bookstore, the probability distributions of the number of books they will buy are given below. Assuming that Joe and Matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore?

• 0.0625

• 0.1250

• 0.1875

• 0.2500

• 0.7500

A fair coin is to be flipped 5 times. The first 4 flips land "heads" up. What is the probability of "heads" on the next (5th) flip of this coin?

• 1

• 1/2

• (5/1)(1/2)^4(1/2)

• (1/2)^4(1/2)

• 0

For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays?

• 0.065

• 0.335

• 0.350

• 0.450

• 0.665

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

Ms. Tucker travels through two intersections with traffic lights as she drives to the market. The traffic lights operate independently. The probability that both lights will be red when she reaches them is 0.22. The probability that the first light will be red and the second light will not be red is 0.33. What is the probability that the second light will be red when she reaches it?

• 0.40

• 0.45

• 0.50

• 0.55

• 0.60

Which of the following statements is true for two events, each with probability greater than 0?

• If the events are mutually exclusive, they must be independent.

• If the events are independent, they must be mutually exclusive.

• If the events are not mutually exclusive, they must be independent.

• If the events are not independent, they must be mutually exclusive.

• If the events are mutually exclusive, they cannot be independent.

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?

• 2/36

• 3/36

• 3/15

• 2/9

• 4/6

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