1. Consider the event that a player scores a point in a game against team A and the event that the same player scores a point in a game against team B. What is the union of the two events? What is the intersection of the two events?

2.8 Ford Motor Company advertises its cars on radio and on television. The company is interested in assessing the probability that a randomly chosen person is exposed to at least one of these two modes of advertising. If we define event R as the event that a randomly chosen person was exposed to a radio advertisement and event T as the event that the person was exposed to a television commercial, define R U T and R ∩ T in this context.

1. Following are age and sex data for 20 midlevel managers at a service company: 34 F, 49 M, 27 M, 63 F, 33 F, 29 F, 45 M, 46 M, 30 F, 39 M, 42 M, 30 F, 48 M, 35 F, 32 F, 37 F, 48 F, 50 M, 48 F, 61 F. A manager must be chosen at random to serve on a companywide committee that deals with personnel problems. What is the probability that the chosen manager will be either a woman or over 50 years old or both? Solve both directly from the data and by using the law of unions. What is the probability that the chosen manager will be under 30?
   2.24 A cross-tabulation of all the students at a small liberal arts college by gender and by school year is below. A student is selected at random. What is the probability that the selected student is
   
   1. a sophomore or male? (Express your answer as a fraction.)
      
   2. A female senior?

1. A female senior or a male junior?
2. A sophomore given that the student is female?
3. A male given that the student is a junior?
4. A male and not a junior?
5. A male given that the student is not a junior?

Freshman Sophomore Junior Senior Total

Male 310 291 189 172 962

Female 338 306 238 230 1112

Total 648 597 427 402 2074

1. An express delivery service promises overnight delivery of all packages checked in before 5 p.m. The delivery service is not perfect, however, and sometimes delays do occur. Management knows that if delays occur in the evening flight to a major city from which distribution is made, then a package will not arrive on time with probability 0.25. It is also known that 10% of the evening flights to the major city are delayed. What percentage of the packages arrive late? (Assume that all packages are sent out on the evening flight to the major city and that all packages arrive on time if the evening flight is not delayed.)

1. A package of documents needs to be sent to a given destination, and delivery within one day is important. To maximize the chances of on-time delivery, three copies of the documents are sent via three different delivery services. Service A is known to have a 90% on-time delivery record, service B has an 88% on-time delivery record, and service C has a 91% on-time delivery record. What is the probability that at least one copy of the documents will arrive at its destination on time?

1. A device has three components and works as long as at least one of the components is functional. The reliabilities of the components are 0.96, 0.91, and 0.80. What is the probability that the device will work when needed?

1. In a takeover bid for a certain company, management of the raiding firm believes that the takeover has a 0.65 probability of success if a member of the board of the raided firm resigns, and a 0.30 chance of success if she does not resign. Management of the raiding firm further believes that the chances for a resignation of the member in question are 0.70. What is the probability of a successful takeover?

1. A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm system sounds with the probability 0.02. A real emergency situation is a rare event, with probability 0.004. Given that the alarm has just sounded, what is the probability that a real emergency situation exists?

1. A company has four departments: manufacturing, distribution, marketing, and management. The number of people in each department is 55, 30, 21, and 13, respectively. Each department is expected to send one representative to a meeting with the company president. How many possible sets of representatives are there?

1. Megabucks is a lottery game played in Massachusetts with the following rules. A random drawing of 6 numbers out of all 36 numbers from 1 to 36 is made every Wednesday and every Saturday. The game costs $1 to play, and to win a person must have the correct six numbers drawn, regardless of their order. (The numbers are sequentially drawn from a bin and are arranged from smallest to largest. When a player buys a ticket prior to the drawing, the player must also arrange his or her chosen numbers in ascending order.) The jackpot depends on the number of players and is usually worth several million dollars. What is the probability of winning the jackpot?

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