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A ________ is the probability that one event will occur given that we know that another event already has occurred.

• conditional probability

• long-run relative frequency

• subjective probability

• sample space outcome

The ________ of two events X and Y is another event that consists of the sample space outcomes belonging to either event X or event Y or both events X and Y.

• conditional probability

• complement

• union

• 
  intersection

Which approach to probability is exemplified by the following formula?

Probability of an event =

• The subjective approach

• The empirical approach

• The classical approach

• 
  None of these answers are correct.

Giorgio offers the person who purchases an unce bottle of Allure two free gifts, chosen from the following: an umbrella, a 1-ounce bottle of Midnight, a feminine shaving kit, a raincoat, or a pair of rain boots. If you purchased Allure, what is the probability you randomly select an umbrella and a shaving kit in that order?

• 1.00

• 0.05

• 0.20

• 0.00

Answer explanation

There are five different gifts. Therefore, the probability of any gift is 1/5 = 0.2. The probability of selecting a second gift is a conditional probability that assumes the first selection was an umbrella, so the probability of a second gift, a shaving kit, is 1/4 = 0.25. The joint probability is (1/5)(1/4) = 1/20 = 0.05.

A firm offers routine physical examinations as part of a health service program for its employees. The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work, and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work?

• 0.50

• 0.20

• 0.25

• 1.00

Answer explanation

The two events, corrective shoes and dental work, are not mutually exclusive because an employee can need both. The P(corrective shoes or dental work) = P(corrective shoes) + P(dental work) − P(corrective shoes and dental work) = 0.8 + 0.15 − 0.03 = 0.20.

There are 10 AAA batteries in a box and 3 are defective. Two batteries are selected without replacement. What is the probability of selecting a defective battery followed by another defective battery?

• 1/4 or 0.25

• 1/120 or about 0.0083

• 1/2 or 0.50

• 1/15 or about 0.07

Answer explanation

The probability of a defective battery on the first selection is 3/10 = 0.3. The probability of selecting a second defective battery is a conditional probability that assumes the first selection was defective, so the probability of a second defective battery is 2/9. The joint probability is (3/10)(2/9) = 0.066667.

In a finance class, the final grade is based on three tests. Historically, the instructor tells the class that the joint probability of scoring As on the first two tests is 0.5. A student assigns a probability of 0.9 that she will get an A on the first test. What is the probability that the student will score an A on the second test given that she scored an A on the first test?

• 
  0.56

• 0.50

• 0.95

• 0.90

Answer explanation

The general rule of multiplication states that P(A and B) = P(A|B) P(B), so P(A|B) = P(A and B)/P(B). Therefore, P(A on second test| A on first test) = P(A on both tests) / P(A on first test) = 0.5/0.9 = 0.56.

In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT attend college?

• 0.20

• 
  0.25

• 0.80

• 
  0.08

Answer explanation

First, the conditional probability that a person attended college given the person is female is P(college | female) = 0.9. The complement is P(no college | female) = 0.1. Now the joint probability of selecting a female who did not attend college is P(female and no college) = P(female) P(no college | female) = (0.8)(0.1) = 0.08.

• 0.404

• 0.60

• 
  0.45

• 0.27

Answer explanation

This is a conditional probability: P(excellent potential | above-average ability)(135/300) = 0.45. There are 300 salespeople who are above average; 135 have excellent potential.

The probability of rolling a 3 or 2 on a single die is an example of conditional probability.

• True
• False