A teacher has three sections of a history course. In section A there are 18 students, and 15 of them passed. In section B there are 14 students, and 13 of them passed. In section C there are 19 students, and 17 of them passed. Given that a student did not pass, what is the probability that the student came from section A?

If we choose one of the teacher's students at random, what is the probability that the student passed?

Suppose we took a poll and asked 100 students to name their favorite TV program. The answers are:

Given that a student picked the Simpsons, what is the probability that the student is in 9th or 10th grade?

A discrete probability distribution has five possible events. The probabilities of events A, B, C, and D are .2, .3, .4, and .1, respectively. What is the probability of event E?

Suppose that the probability of the Redskins having a winning season is .5 and the probability that both the Redskins and the Capitals will have a winning season is .3. If the two events are independent, what is the probability that the Capitals will have a winning season?

A bank uses a 3-digit PIN number for its ATM cards. How many possible PIN numbers are there (using only the numbers 0-9, not letters)? The ATM machine lets the user try to enter a PIN number 4 times before it confiscates the card. What is the probability that someone will be able to guess a PIN number before the machine confiscates the card?

Suppose that a test for ulcer will indicate an ulcer 98 percent of the time when an ulcer is present. The test also will indicate an ulcer 1 percent of the time when an ulcer is not present (this type of result is called a false positive). Suppose that 7 percent of people actually have ulcers.

• What is the probability that a person selected at random will test positive for an ulcer?
• What is the probability that a person who tests positive actually will have the disease?