1.LetAandBbe two events in a sample spaceSsuch thatP(A) =0.6,P(B) =0.5, andP(AB) =0.15. Find the probabilities below.

(a)P(A|B^c)

(b)P(B|A^c)

2.IfAandBare independent events,P(A) =0.25, andP(B) =0.55, find the probabilities below. (Enter your answers to four decimal places.)

(a)P(AB)

(b)P(AB)

(c)P(A|B)

(d)P(A^cB^c)

3.A pair of fair dice is rolled. LetEdenote the event that the number falling uppermost on the first die is2, and letFdenote the event that the sum of the numbers falling uppermost is8. (Round your answers to three decimal places.)

(a) ComputeP(F).

(b) ComputeP(EF).

c) ComputeP(F|E)

(d) ComputeP(E).

4.Jack has decided to advertise the sale of his car by placing flyers in the student union and the dining hall of the college. He estimates that there is a probability of0.3that a potential buyer will read the advertisement and that, if it is read, the probability that the reader will buy his car will be0.2. Using these estimates, find the probability that a potential buyer will read the ad and will buy Jack's car.

5.A tax specialist has estimated that the probability that a tax return selected at random will be audited is0.05. Furthermore, he estimates the probability that an audited return will result in additional assessments being levied on the taxpayer is0.60. What is the probability that a tax return selected at random will result in additional assessments being levied on the taxpayer?

6.The personnel department of Franklin National Life Insurance compiled the accompanying data regarding the income and education of its employees.

Income$60,000 or BelowIncome Above $60,000

Noncollege Graduate 2010. 840

College Graduate 400. 750

LetAbe the event that a randomly chosen employee has a college degree, and letBbe the event that the chosen employee's income is more than $60,000. Find each of the following probabilities. (Round your answers to four decimal places.)

a)P(A)=

b)P(B)=

C)P(AB)=

D)P(B|A)=

E)P(B|A^c)=

7.A coin is tossed three times.

(a) What is the probability that the coin will landheadsat least twice?

(b) What is the probability that the coin will landheadson the second toss, given thatheadswere thrown on the first toss?

(c) What is the probability that the coin will landheadson the third toss, given thattailswere thrown on the first toss?

8.An automobile manufacturer obtains the microprocessors used to regulate fuel consumption in its automobiles from three microelectronic firms:A,B, andC. The quality-control department of the company has determined that7%of the microprocessors produced by firmAare defective,3%of those produced by firmBare defective, and9.5%of those produced by firmCare defective. FirmsA,B, andCsupply35%,20%, and45%, respectively, of the microprocessors used by the company. What is the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor?

9.Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is aspadegiven that the second card is adiamond? (Round your answer to three decimal places.)

10.Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a face card (jack, queen, or king) given that the second card is anace? (Round your answer to three decimal places.)

11.Data compiled by the Highway Patrol Department regarding the use of seat-belts by drivers in a certain area after the passage of a compulsory seat-belt law are shown in the accompanying table. (Round your answers to three decimal places.)

Percentage ofDrivers

in Group Percent of Group Stopped

for Moving Violation

Group I

(using seat-belts). 70 0.2

Group II

(not using seat-belts) 30 0.5

(a) If a driver in that area is stopped for a moving violation, what is the probability that he or she will have a seat-belt on?

(b) If a driver in that area is stopped for a moving violation, what is the probability that he or she will not have a seat-belt on?

12.In a recent senatorial election,59%of the voters in a certain district were registered as Democrats,38%were registered as Republicans, and3%were registered as Independents. The incumbent Democratic senator was reelected over her Republican and Independent opponents. Exit polls indicated that she gained75%of the Democratic vote,25%of the Republican vote, and27%of the Independent vote. Assuming that the exit poll is accurate, what is the probability that a vote for the incumbent was cast by a registered Republican? (Round your answer to three decimal places.)