Question

1.The probability that an employee at a company eats lunch at the company cafeteria is 0.23, and the probability that employee is female is 0.52. Assume the probability that an employee eats lunch at the company cafeteria and is female is 0.11.

a) What is the probability that a randomly chosen employee either eats lunch at the company cafeteria or is female?

b) Are eating lunch at the company cafeteria and gender of a randomly chosen employee mutually exclusive events?

2.In a survey of top executives, it was found that 17% had traveled internationally

on business. The probability of one of these executives fluently speaking a foreign language was found to be 10%. The probability that one of these executives neither spoke a foreign language nor had traveled internationally was 0.81. What is the probability that an executive who speaks a foreign language has traveled internationally?

3.You can order a new model of an electronic notebook in one of five colors. The notebook also comes loaded with one of four different games. How many different combinations of colors and games are possible? If you were to order three different notebooks without stating preference on color or games, what is the probability that they are identical? Assume that the color and game on one notebook is independent of any others.

4.Firms are increasingly asking applicants to submit to drug tests. Suppose that drug tests can identify a drug user 98% of the time. However, 1% of the time the test indicates a positive result although the applicant is not a drug user. If 10% of all applicants are drug users, what is the probability that a person who has tested positive for drug use is not really a drug user?

Answer 1

1.The probability that an employee at a company eats lunch at the company cafeteria is 0.23, and the probability that employee is female is 0.52. Assume the probability that an employee eats lunch at the company cafeteria and is female is 0.11.

a) What is the probability that a randomly chosen employee either eats lunch at the company cafeteria or is female?

b) Are eating lunch at the company cafeteria and gender of a randomly chosen employee mutually exclusive events?

a)

P( either eats lunch or is female) = P(eats lunch) + P(Female)- P(eats lunch and is female)

=0.23+0.52-0.11=0.64

b)

no,eating lunch at the company cafeteria and gender of a randomly chosen employee are not mutually exclusive events

for mutually exclusive events,P(A and B) should be 0.

but here it is not zero,so not mutually exclusive events