Exam 5: A Survey of Probability Concepts

An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight. What is the probability of selecting three packages that are satisfactory?

When are two experimental outcomes mutually exclusive?

The joint probability of two events, A and B, that are not independent is computed as P(A and B) = P(A) P(B|A).

A cell phone salesperson has kept records on the customers who visited his store. Forty percent of the customers who visited the store were female. Furthermore, the data show that 35% of the females who visited his store purchased a cell phone, while 20% of the males who visited his store purchased a cell phone. Let A₁ represent the event that a customer is a female, A₂ represent the event that a customer is a male, and B represent the event that a customer will purchase a phone. What is the probability that a male customer will purchase a cell phone?

A coin is tossed four times. The joint probability that all four tosses will result in a head is ¼ or 0.25.

The ABCD football association is considering a Super Ten Football Conference. The top 10 football teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. How many games would the conference commissioner have to schedule each year? (Remember, Oklahoma versus Michigan is the same as Michigan versus Oklahoma.)

A cell phone salesperson has kept records on the customers who visited his store. Forty percent of the customers who visited the store were female. Furthermore, the data show that 35% of the females who visited his store purchased a cell phone, while 20% of the males who visited his store purchased a cell phone. Let A₁ represent the event that a customer is a female, A₂ represent the event that a customer is a male, and B represent the event that a customer will purchase a phone. What is the probability that a female customer will purchase a cell phone?

A company set up a kiosk in the Mall of America for several hours and asked randomly selected people which color cell phone cover was their favorite. The results follow: What is the probability that red is the favorite color, given that the person's age is 21 or older?

In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT attend college?

How many permutations of the three letters C, D, and E are possible?

The complement rule states that the probability of an event not occurring is equal to one minus the probability of its occurrence.

An electronics firm sells four models of stereo receivers, three amplifiers, and six speaker brands. When the four types of components are sold together, they form a "system." How many different systems can the electronics firm offer?

In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who attended college?

If P(A) = 0.62, P(B) = 0.47, and P(A or B) = 0.88, then P(A and B) = _____.