Probability Concepts and Applications test bank

2.110 An urn contains 7 blue and 3 yellow chips. If the drawing of chips is done with replacement, determine the probability of:

(a) drawing three yellow chips

(b) drawing a blue chip on the first draw and a yellow chip on the second draw

(c) drawing a blue chip on the second draw given that a yellow chip was drawn on the first draw

(d) drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw

(e) drawing a yellow chip on the second draw given that a yellow chip was drawn on the first draw

2.111 A market research study is being conducted to determine if a product modification will be
well received by the public. A total of 1,000 consumers are questioned regarding this product.
The table below provides information regarding this sample.

	Positive Reaction	Neutral Reaction	Negative Reaction
Male	240	60	100
Female	260	220	120

(a) What is the probability that a randomly selected male would find this change unfavorable (negative)?

(b) What is the probability that a randomly selected person would be a female who had a positive reaction?

(c) If it is known that a person had a negative reaction to the study, what is the probability that the person is male?

2.112 In a production run of 300 units, there are exactly 20 defective items and 280 good items.

(a) What is the probability that a randomly selected item is defective?

(b) If two items are sampled without replacement, what is the probability that both are good?

(c) If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective?

2.113 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?

2.114 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?

2.115 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?

2.116 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.

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2.117 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?

2.118 Fast Service Store has maintained daily sales records on the various size "Cool Drink" sales.
Assuming that past performance is a good indicator of future sales,

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

(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" ?

2.119 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

2.120 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

2.121 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?

2.122 Arrivals in a university advising office during the week of registration are known to follow a Poisson distribution with an average of 4 people arriving each hour.

(a) What is the probability that exactly 4 people will arrive in the next hour?

(b) What is the probability that exactly 5 people will arrive in the next hour?

2.123 Explain why event probabilities range from zero to one.

2.124 Using a standard deck of 52 cards, explain why the situation of drawing a 7 and a club is not collectively exhaustive.

2.125 Name five common probability distributions.

2.126 If two events (A,B) are mutually exclusive, what is the probability of event A or event B occurring?

2.127 If two events (A,B) are not mutually exclusive, what is the probability of event A or event B occurring?

2.128 If two events (A,B) are independent, what is their joint probability?

2.129 If two events (A,B) are dependent, what is the conditional probability of P(A|B)?

2.130 If two events (A,B) are independent, then the conditional probability of P(A|B) =

2.131 Explain what a discrete random variable is.

2.132 The exponential distribution often describes _______________________________.

2.133 List the two parameters of the normal distribution.

2.134 In what way is the F distribution often used?

2.135 List the parameter(s) of the Poisson distribution.