Classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

• 3.1. On the basis of prior counts, a quality control officer says there is a 0.05 probability that a randomly chosen part is defective.

Find the probability of the sequence of events.

• 3.2. You are shopping, and your roommate has asked you to pick up toothpaste and dental rinse. However, your roommate did not tell you which brands to get. The store has eight brands of toothpaste and five brands of dental rinse. What is the probability that you will purchase the correct brands of both products. Is this an unusual event? Explain.

Determine the probability

• 3.3. A card is randomly selected from a standard deck. Find the probability that the card is between 4 and 8, inclusive, or is a club.

Use combinations and permutations.

• 3.4. An employer must hire 2 people from a list of 13 applicants. In how many ways can the employer choose to hire the 2 people.

Decide whether the distribution is a probability distribution. If it is not, identify the property that is not satisfied.

• 4.1. The daily limit for caching bass at a lake is four. The random variable x represents the number of fish caught in a day.

x 0 1 2 3 4

P(x) 0.36 0.23 0.08 0.14 0.29

Decide whether the experiment is a binomial experiment. If it is not, identify the property that is not satisfied. If it is, list the values of n,p, and q and the values that x an assume.

• 4.2. Forty-three prevent of businesses in the United States require a doctors note when an employee takes sick time. You randomly select nine businesses and ask each if it requires a doctors note when an employee takes sick time. Find the probability that the number who say they require a doctors note is (a) exactly five, (b) at least five, and (c) more than five.