Exam 4: Introduction to Probability

If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then P(A $\cup$ B) =

A government agency has 6,000 employees. The employees were asked whether they preferred a four-day work week (10 hours per day), a five-day work week (8 hours per day), or flexible hours. You are given information on the employees' responses broken down by sex. a. What is the probability that a randomly selected employee is a man and is in favor of a four-day work week? b. What is the probability that a randomly selected employee is female? c. A randomly selected employee turns out to be female. Compute the probability that she is in favor of flexible hours. d. What percentage of employees is in favor of a five-day work week? e. Given that a person is in favor of flexible time, what is the probability that the person is female? f. What percentage of employees is male and in favor of a five-day work week?

A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select?

Six vitamin and three sugar tablets identical in appearance are in a box. One tablet is taken at random and given to Person A. A tablet is then selected and given to Person B. What is the probability that a. Person A was given a vitamin tablet? b. Person B was given a sugar tablet given that Person A was given a vitamin tablet? c. neither was given vitamin tablets? d. both were given vitamin tablets? e. exactly one person was given a vitamin tablet? f. Person A was given a sugar tablet and Person B was given a vitamin tablet? g. Person A was given a vitamin tablet and Person B was given a sugar tablet?

Ten individuals are candidates for positions of president, vice president of an organization. How many possibilities of selections exist?

If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A | B) =