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58) A survey of 100 students at a large university found that 80 students played tennis, 43 played basketball, and

35 played both tennis and basketball. If a students is selected at random, what is the (empirical) probability

that the student plays neither tennis nor basketball?

59) A group of 10 people consists of 5 men and 5 women. A committee of 4 is chosen from this group. What is the

probability that one or more of the committee members is a man?

60) A shipment of 28 compact disc players contains 4 that are defective. If 7 players from this shipment are

selected at random and tested, what is the probability that at least one defective player will be found?

61) The odds in favor of event A are 3:5. What is the probability of A'?

62) A survey of men and women pet owners found that 25 owned a dog, 35 owned a cat, 4 owned a bird, and 1

owned a gerbil. Of the women, 10 owned a dog, 15 owned a cat, 4 owned a bird, and 0 owned a gerbil. No

person owned more than one pet. What is the probability that a person chosen at random from this group is

male and owned a cat or a dog?

63) From a survey involving 2,000 students at a large university, it was found that 1,300 students had classes on

Monday, Wednesday, and Friday; 1,500 students had classes on Tuesday and Thursday; and 800 students had

classes every day. If a student at this university is selected at random, what is the (empirical) probability that

the student has classes only on Tuesday and Thursday?

64) A class of 40 students has 10 honor students and 13 athletes. Three of the honor students are also athletes.

One student is chosen at random. Find the probability that this student is an athlete if it is known that the

student is not an honor student.

65) A group of 25 people contains 10 brunettes, 8 blondes, and 7 redheads. Of the 20 girls in the group, 8 are

brunettes, 6 are blondes, and 6 are redheads. A person is selected at random. Are the events of being a girl and

having brown hair independent?

66) A box contains 7 red balls and 3 white balls. Two balls are to be drawn in succession without replacement.

What is the probability that the sample will contain exactly one white ball and one red ball?

67) In building the space shuttle, NASA contracts for certain guidance components to be supplied by three

different companies: 41% by company A, 25% by company B, and 34% by company C. It has been found that

1%, 1.75%, and 2% of the components from companies A, B, and C, respectively, are defective. If one of these

guidance components is selected at random, what is the probability that it is defective?

68) One urn has 4 red balls and 1 white ball; a second urn has 2 red balls and 3 white balls. A single card is

randomly selected from a standard deck. If the card is less than 5 (aces count as 1), a ball is drawn out of the

first urn; otherwise a ball is drawn out of the second urn. If the drawn ball is red, what is the probability that

it came out of the second urn?

69) A small manufacturing company has rated 75% of its employees as satisfactory (S) and 25% as unsatisfactory.

Personnel records show that 80% of the satisfactory workers had previous work experience (E) in the job they

are now doing, while 15% of the unsatisfactory workers had no work experience (E') in the job they are now

doing. If a person who has had previous work experience is hired, what is the approximate empirical

probability that this person will be an unsatisfactory employee?

Math Exam Final Review Worksheet With Answer Key - M118, Indiana University Southeast Page 6