EXAM 3
Math 141-527
Nov. 18, 1999

Name
SSN

1. Answer each of the following questions: (2 pts each)
   TFIf S is the sample space of an experiment then P(S)= 0.
   TFIf E is any event then .
   TFFor any event E, 0<P(E)<1.
   TFFor two events E and F, .
   TFTwo events E and F are mutually exclusive if and only if .
2. Suppose an experiment consists of rolling two (fair) four-sided dice and recording the sum of the numbers which fall uppermost.
   1. (2 pts) Write down the sample space for this experiment.
   2. (2 pt) Is each outcome in this sample space equally likely?
   3. (4 pts) Assign a probability distribution for this sample space.

3. Suppose an experiment consists of rolling two, fair, six-sided dice, one of which is red, the other green. Let .
   1. (4 pts) Assign a probability distribution for X.
   2. (3 pts) Sketch a histogram for X.

4. Among 825 freshmen pursuing a business degree at Podunk University:
   460 are enrolled in a Mathematics course,
   365 are enrolled in a Chemistry course,
   487 are enrolled in an English course,
   170 are enrolled in both English and Mathematics,
   272 are enrolled in both Chemistry and Mathematics,
   193 are enrolled in both Chemistry and English and
   111 are enrolled in all three types of courses.
   You will need a Venn Diagram. (4 pts)

   What is the probability that a freshmen selected at random from this group is enrolled in

   1. an English and/or a Mathematics course? (3 pts)
   2. exactly two of the three types of courses? (3 pts)
   3. none of the courses? (3 pts)

5. Microsoft Corp. and Oracle Corp. are putting on a computer show. Microsoft sends 47 people to the show and Oracle sends 23 people to the show. It is decided that a six person committee should be formed to handle public relations for the show. This committee is to be formed by choosing randomly among the Microsoft and Oracle attendees. If Yolanda is a Microsoft attendee and Bubba is an Oracle attendee what is the probability that
   
   1. (5 pts) Yolanda will be chosen to be on the committee if there are no other restrictions on how the committee may be formed?
   2. (5 pts) both Yolanda and Bubba will be chosen if the committee must be made up of equal numbers of Microsoft and Oracle attendees?

6. A teacher writes a quiz which has 10 multiple choice problems on it, where each question has four possible answers. If a student is completely lost and fills in each answer randomly, what is the probability of getting at least 8 answers correct? (7 pts)
7. The Legislative branch of the U.S. government has 535 members. Of these, 100 are Senators and 435 are Representatives. The Senate has 56 Republicans and the House of Representatives has 220 Republicans (the rest, in both houses, are Democrats). If a legislator is chosen at random what is the probability that
   1. the legislator is a Republican? (4 pts)
   2. the legislator is a Democrat if it is known that they are a representative? (4 pts)
   3. the legislator is a Senator if it is known that they are Republican? (4 pts)

8. Mr. Hunt is considering two business ventures. The anticipated returns (in thousands of dollars) of each venture are described by the following probability distributions.

   

   

   1. Compute the mean and standard deviation for each venture. (6 pts)
   2. Which investment would provide Mr. Hunt with the higher expected return? (3 pts)
   3. Which investment would the element of risk be less? (that is, where is the deviation away from the mean, the least?) (3 pts)

9. It is estimated that one-third of the general population has blood type .
   1. If a sample of nine people is selected at random what is the probability that at most two of them have blood type ? (5 pts)
   2. If blood is needed for a transfusion how many people should be selected to donate blood in order to assure a 95% probability that at least on of them will be ? (6 pts)

10. Data compiled by the Department of Justice on the number of people arrested for violent crimes in 1990 revealed that 88% were male and 12% were female. Of the males, 30% were under 18, whereas 27% of the females arrested were under 18.
    1. If a person arrested for a serious crime in 1990 was known to be under 18, what is the probability that they were female? (6 pts)
    2. What is the probability that a person arrested for a violent crime in 1990 was under 18? (4 pts)

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