### MAT 119 7.3 Rules of Probability

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TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS

1. A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)

The sum of the numbers is either 7 or 11.

1. A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment, and find the probability of the given event. (Enter your answer as a fraction.)

The sum of the numbers is at least 4.

1. An experiment consists of selecting a card at random from a 52-card deck. Refer to this experiment and find the probability of the event. (Enter your answer as a fraction.)

A diamond or a queen is drawn.

1. The results of a recent television survey of American TV households revealed that 89 out of every 100 TV households have at least one remote control. What is the probability that a randomly selected TV household does not have at least one remote control? (Enter your answer as a fraction.)

2. Is the statement correct?

The probability that a bus will arrive late at the Civic Center is 0.4, and the probability that it will be on time or early is 0.53.

1. Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.5, P(F) = 0.4, and P(E ? F) = 0.2. Compute the values below.

2. In a survey of 200 employees of a company regarding their 401(k) investments, the following data were obtained.

66had investments in money market funds.

52had investments in stock funds and bond funds.

34had investments in stock funds and money market funds.

35had investments in bond funds and money market funds.

23had investments in stock funds, bond funds, and money market funds.

(a) What is the probability that an employee of the company chosen at random had investments in exactly two kinds of investment funds? (Enter your answer to three decimal places.)

(b) What is the probability that an employee of the company chosen at random had investments in exactly one kind of investment fund? (Enter your answer to two decimal places.)

(c) What is the probability that an employee of the company chosen at random had no investment in any of the three types of funds? (Enter your answer to three decimal places.)

1. Among 500 freshmen pursuing a business degree at a university, 309 are enrolled in an economics course, 229 are enrolled in a mathematics course, and 135 are enrolled in both an economics and a mathematics course. What is the probability that a freshman selected at random from this group is enrolled in each of the following? (Enter your answers to three decimal places.)

(a)an economics and/or a mathematics course

(b)exactly one of these two courses

(c)neither an economics course nor a mathematics course

1. According to a study conducted in 2003 concerning the participation, by age, of 401(k) investors, the following data were obtained:

Age 20s 30s 40s 50s 60s

Percent 10 25 34 21 10

(a) What is the probability that a 401(k) investor selected at random was in his or her 20s or 60s?

(b) What is the probability that a 401(k) investor selected at random was under the age of 50?

1. In a survey conducted to see how long Americans keep their cars, 2000 automobile owners were asked how long they plan to keep their present cars. The results of the survey follow. Find the probability distribution associated with these data. (Enter your answers to four decimal places.)

What is the probability that an automobile owner selected at random from those surveyed plans to keep his or her present car:

(a)Less than five years?

(b)3 years or more?

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