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Probability & Statistics

1. Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverages, 216 east between meals, 122 smoke and drink alcoholic beverages, 83 east between meals and drink alcoholic beverages, 97 smoke and eat between meals, and 52 engage in all three of these bad health practices. If a member of this senior class is selected at random, find the probability that the student

a) smokes but does not drink alcoholic beverages;

b) eats between meals and drinks alcoholic beverages but does not smoke;

c) neither smokes nor eats between meals.

2. An automobile manufacturer is concerned about a possible recall of its best-selling four-door sedan. If there were a recall, there is 0.25 probability that a defect is in the brake system, 0.18 in the transmission, 0.17 in the fuel system, and 0.40 in some other area.

a) What is the probability that the defect is the brakes or the fueling system if the probability of defects in both systems simultaneously is 0.15?

b) What is the probability that there are no defects in either the brakes or the fueling system?

3. A pair of fair dice is tossed. Find the probability of getting

a) a total of 8;

b) at most a total of 5.

4. Dom's Pizza Company uses taste testing and statistical analysis of the data prior to marketing any new product. Consider a study involving three types of crusts (thin, thin with garlic and oregano, and thin with bits of cheese). Dom's is also studying three sauces, (standard, a new sauce with more garlic, and a new sauce with fresh basil).

a) How many combinations of crust and sauce are involved?

b) What is the probability that a judge will get a plain thin crust with a standard sauce for his first taste test?

5. Interest centers around the life of an electronic component. Suppose it is known that the probability that the component survives for more than 6000 hours is 0.42. Suppose also that the probability that the component survives no longer than 4000 hours is 0.04.

a) What is the probability that the life of the component is less than or equal to 6000 hours?

b) What is the probability that the life is greater than 4000 hours?

6. Factory workers are constantly encouraged to practice zero tolerance when it comes to accidents in factories. Accidents can occur because the working environment or conditions themselves are unsafe. On the other hand, accidents can occur due to carelessness or so-called human error. In addition, the worker's shift 7am - 3pm (day shift), 3pm - 11pm (evening shift), 11pm - 7am (graveyard shift), may be a factor. During the last year, 300 accidents have occurred. The percentages of the accidents for the condition combinations are as follows:

Shift Unsafe Conditions Human Error
Day 5% 32%
Evening 6% 25%
Graveyard 2% 30%

a) What is the probability that the accident occurred on the graveyard shift?

b) What is the probability that the accident occurred due to human error?

c) What is the probability that the accident occurred due to unsafe conditions?

d) What is the probability that the accident occurred on either the evening or graveyard shift?

7. Interest centers around the nature of an oven purchased at a particular department store. It can be either a gas or electric oven. Consider the decision made by six distinct customers.

a) Suppose that the probability is 0.40 that at most, two of these individuals purchase an electric oven. What is the probability that at least three purchase the electric oven?

b) Suppose it is known that the probability that all six purchase the electric oven is 0.007 while 0.104 is the probability that all six purchase the gas oven. What is the probability that at least one of each type is purchased?

8. In an experiment to study the relationship of hypertension and smoking habits, the following date are collected for 180 individuals:

Non Smokers Moderate Smokers Heavy Smokers
H 21 36 30
NH 48 26 19

Where H and NH in the table stand for Hypertension and Nonhypertension, respectively. If one of these individuals is selected at random, find the probability that the person is

a) experiencing hypertension, given that the person is a heavy smoker;

b) a nonsmoker, given that the person is experiencing no hypertension.

9. For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, the probability that his wife will vote in the referendum is 0.28, and the probability that both the husband and wife will vote is 0.15. What is the probability that

a) at least one member of a married couple will vote?

b) a wife will vote, given that her husband will vote?

c) a husband will vote, given that his wife does not vote?

10. The probability that the head of a household is home when a telemarketing representative calls is 0.4. Given that the head of the house is home, the probability that goods will be bought from the company is 0.3. Find the probability that the head of the house is home and goods being bought from the company.

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