Exam 9: Introduction to Probability and Statistics

Two cards are randomly drawn with replacement from a standard deck of 52 playing cards.Find the probability that (a)both cards are aces; (b)the first card is red and the second card is a club; (c)one card is red and the other is a club.

The number of ways in which a student can answer an eight-question true-false examination is

If P(E)= 0.3,P(F)= 0.4, P(E ∩ F). F)= 0.2, find P(E ∪

An urn contains ten marbles numbered 1 through 10.If two marbles are randomly drawn in succession without replacement,determine the probability that (a)the first marble drawn shows 1 and the second shows 2; (b)both show an odd number; (c)at least one marble shows a number greater than 5.

A manufacturer of widgets has three assembly lines: A,B,and C.The percentages of total daily output that are produced by the lines are 25%,35%,and 40%,respectively.The percentages of defective units produced by the lines are estimated to be 1%,2%,and 1%,respectively.If a widget is randomly selected from a day's production,what is the probability that it is defective?

A certain disease is believed to affect 4% of the population.Results of a new blood test for the disease indicate that 95% of persons who have the disease will have a positive reaction to the test,whereas 5% of those who do not have the disease will also have a positive reaction.What is the probability that a randomly selected person who has a positive reaction will actually have the disease?

A United Nations diplomat can travel from Washington,D.C.to New York City in 6 ways.Depending on the urgency of the trip,she can fly by helicopter,fly by plane,drive the car to a suburban subway station and then take the subway the rest of the way,drive by limousine,take the train,or borrow a friend's yacht and sail most of the way.When she returns to Washington,D.C.,the same modes of transportation are available.How many round trip transportation combinations are available to her?

A state legislative body is considering an action that allows gambling within the state.An opinion survey of 200 voters was conducted and the results are indicated in the following table: Favor Oppose No Opinion Total Democrat 40 35 9 84 Republican 60 30 6 96 Other 4 8 8 20 Total 104 73 23 200 Assume that the survey reflects the opinion of the voting population.If a person is selected at random,determine each of the following (empirical)probabilities: (a)P (opposes gambling) (b)P (Republican) (c)P (Democrat who favors gambling).

A student must select two courses in the liberal arts and three courses in the social sciences.There are six liberal arts courses and ten social science courses,all of which are different,from which the student may choose.How many selections are possible?

Two cards are randomly drawn with replacement from a standard deck of 52 cards.Find the probability of drawing,in order,the queen of hearts and a diamond.

If the probability that a certain horse wins a race is ,find the odds that this event occurs.

The probability that Bob survives ten more years is ,and the probability that Mary survives ten more years is .Find the probability that exactly one of them survives ten more years.(Assume independence.)

A quiz contains four multiple-choice problems.Each problem has five choices for the answer,but only one of them is correct.If a student randomly guesses the answer to each problem,find the probability that the student gets exactly three correct answers.

If a fair die is rolled three times,find the probability of getting an even number each time.

In a certain town,30% of eligible voters are Democrats,40% are Republicans,and the rest are Independents.In the last election,20% of the Democrats,10% of the Republicans,and 30% of the Independents voted.If an eligible voter is chosen at random,what is the probability that he or she is a Republican who voted?

The winner of a contest can choose any two of six different prizes.How many choices are possible?

A plane flies from New York to Chicago,from Chicago to Denver,and from Denver to Los Angeles.The plane's on-time,late,or early departure from each city is recorded as 0 or - or +,respectively.For example,(+,-,0)represents the plane leaving earlier than its scheduled departure time from New York,later than its scheduled departure time from Chicago,and on-time from Denver.Assume that the time ahead of schedule or behind schedule is the same so that the pilot can make up for a late departure.For example,(-,0,+)means the plane was x minutes late out of New York,on-time out of Chicago,and made up the x minutes late out of New York by leaving Denver x minutes early.The plane is,therefore,on time when it arrives in Los Angeles.Determine the following events: (a) = {the plane arrives in L.A.on time} (b) = {the plane is late on arrival in L.A.} (c) = {the plane is on time when it arrives at Denver} (d) = {the plane arrives in L.A.as late as possible} (e) (f) ∪ (g) ∩ (h) ∩ (i) ∪ (j) ∩

In how many ways is it possible to answer a six-question true-false examination.

Determine the value of and simplify your answer.

A fair coin is tossed and then a fair die is rolled.Determine the probability that (a)a head and an odd number show; (b)a 2 or 4 shows.