Exam 4: Probability and Probability Models

Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Also recorded was the proportion of all dinners packed by each employee. Related information is given in the table. What is the probability that Cheryl packed a given dinner and forgot to include a napkin?

What is the probability that an even number appears on the toss of a die?

Three companies produce all the potato chips used by vending machines in public areas in a midwestern state. Company A accounts for 70 percent of the chips, Company B 19 percent, and Company C 11 percent. The probability of the vending company getting an unfilled bag is 2 percent for Company A, 2 percent for Company B, and 4 percent for Company C. Suppose an unfilled bag is found. What is the probability that it came from Company A?

A report on high school graduation stated that 85 percent of high school students graduate. Suppose 3 high school students are randomly selected from different schools. What is the probability that none will graduate?

An auditing firm has developed a set of criteria for determining whether a particular account (and its balance) is in error. Historically, they know that of balances that were in error, 75 percent were regarded as unusual. Assume Company A shows a history of only 10 percent of the account balances being in error and it also shows that 25 percent of the account balances were unusual. If in an audit, a particular account balance appears unusual, what is the probability that it is in error for Company A?

Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Also recorded was the proportion of all dinners packed by each employee. Related information is given in the table. What is the probability that there is not a napkin included for a given order?

Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Also recorded was the proportion of all dinners packed by each employee. Related information is given in the table. You just purchased a dinner and found that there is no napkin in your bag. What is the probability that Cheryl prepared your order?

Bayes' Theorem uses prior probabilities with additional information to compute posterior probabilities.

Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted at University A and rejected at University B?

If a product is made using five individual components, and P(product meets specifications) = P(E) = .98, what is the probability of an individual component meeting specifications, assuming that this probability is the same for all five components?

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club. Are R and C mutually exclusive?

If events A and B are mutually exclusive, calculate P(A|B).

Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted by at least one of the two universities?

A(n) ________ probability is a probability assessment that is based on experience, intuitive judgment, or expertise.

A family has two children. What is the probability that both are girls, given that at least one is a girl?

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club. Are D and C mutually exclusive?

What is the probability of at least one tail in the toss of three fair coins?

A report on high school graduation stated that 85 percent of high school students graduate. Suppose 3 high school students are randomly selected from different schools. What is the probability that all graduate?

A batch of 50 parts contains 6 defects. If two parts are drawn randomly, one at a time, and tested, what is the probability that both parts are defective?

A pair of dice is thrown. What is the probability that one of the faces is a 3, given that the sum of the two faces is 9?