# Chapter 2 Probability Concepts and Applications

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121) A new television program was viewed by 200 people (120 females and 80 males). Of the females, 60 liked the program and 60 did not. Of the males, 60 of the 80 liked the program.

(a) What is the probability that a randomly selected individual liked the program?

(b) If a male in this group is selected, what is the probability that he liked the program?

(c) What is the probability that a randomly selected individual is a female and liked the program?

122) Colonel Motors (an automobile company) has prepared a marketing campaign for its best selling car. The focus of the campaign is quality, and it is claimed that 97 percent of the purchasers of this car have no complaints in the first year. You and your sister Kim have each purchased one of these cars.

(a) What is the probability that neither of you has a complaint about the car in the first year if the advertising claim is true?

(b) What is the probability that exactly one of you has a complaint about the car in the first year if the advertising claim is true?

123) A local "home TV repair service" company has two repairmen who make all of the home repairs. The company sends Repairman D on 70 percent of all jobs, because the likelihood of a "second follow-up call" within a week is only 0.08 compared to 0.20 for Repairman K. If you had a recent repair job that is going to require a second follow-up call, what is the probability that Repairman K did your initial repair work?

124) Our department store is having a sale on personal computers, of which three are in stock (no rain checks). There is a certain probability of selling none. The probability of selling one is twice as great as the probability of selling none. The probability of selling two is three times the probability of selling none. Finally, the probability of selling all the personal computers is four times as great as the probability of selling none. In a table, list the outcomes and their probabilities. Hint: Let the probability of selling none equal x.

125) ABC Manufacturing has 6 machines that perform a particular task. Breakdowns occur frequently for this machine. Past records indicate that the number of breakdowns that occur each day is described by the following probability distribution:

 Number of Breakdowns Probability 0 0.4 1 0.3 2 0.2 3 0.1 More than 3 0.0

(a) What is the expected number of breakdowns in any given day?

(b) What is the variance for this distribution?

(c) What is the probability that there will be at least 2 breakdowns in a day?

126) Fast Service Store has maintained daily sales records on the various size "Cool Drink" sales.

 "Cool Drink" Price Number Sold \$0.50 75 \$0.75 120 \$1.00 125 \$1.25 80 Total 400

Assuming that past performance is a good indicator of future sales,

(a) what is the probability of a customer purchasing a \$1.00 "Cool Drink?"

(b) what is the probability of a customer purchasing a \$1.25 "Cool Drink?"

(c) what is the probability of a customer purchasing a "Cool Drink" that costs greater than or equal to \$1.00?

(d) what is the expected value of a "Cool Drink"?

(e) what is the variance of a "Cool Drink"?

127) In a given office, the color printer breaks down with a probability of 20% in any month. A binomial process is assumed for a period of 10 months.

(a) What is the probability that the printer breaks down exactly 2 times?

(b) What is the probability that the printer breaks down at most 1 time?

(c) What is the probability that the printer breaks down more than once?

128) A southwestern tourist city has records indicating that the average daily temperature in the summer is 82 degrees F, which is normally distributed with a standard deviation of 3 degrees F. Based on these records, determine:

(a) the probability of a daily temperature between 79 degrees F and 85 degrees F.

(b) the probability that the daily temperature exceeds 90 degrees F.

(c) the probability that the daily temperature is below 76 degrees F.

129) Using the table for finding the areas under normal curves, find the area under a normal curve with a mean of 200 and a standard deviation of 10 between the values of:

(a) 200 to 205.

(b) 195 to 205.

(c) 200 to 215.

(d) 195 to 215.

(e) 186.5 to 217.

130) The time required to complete a project is known to be normally distributed with a mean of 44 weeks and a standard deviation of 8 weeks.

(a) What is the probability that the project is finished in 40 weeks or fewer?

(b) What is the probability that the project is finished in 52 weeks or fewer?

(c) There is an 95 percent chance that the project will be finished in fewer than how many weeks?

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## Chapter 2 Probability Concepts and Applications

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