(2 points)

Michael has a box of colored balls. It contains four red balls, six green balls, one purple ball, three yellow balls, and five blue balls. Michael draws a ball at random from the boxLetR denote the event that the ball he draws is red, and letB denote the event that the ball he draws is blue.

What isPr(R|B)?

What isPr(R|B)?

Enter your answers as whole numbers or fractions in lowest terms.

(2 points)

In a study by the Department of Transportation, there were a total of 120 drivers that were pulled over for speeding. Out of those 120 drivers, 30 were men who were ticketed, 25 were men who were not ticketed, 15 were women who were ticketed, and 50 were women who were not ticketed. Suppose one person was chosen at random.

What is the probability that the selected person is a man, given it is someone who was ticketed?

What is the probability that the selected person is someone who was not ticketed, given it is a man?

Enter your answers as whole numbers or fractions in lowest terms.

(2 points)

A bag contains six 1-dollar bills, three 5-dollar bills, and two 10-dollar bills. An experiment consists of drawing three random bills from the bag simultaneously. Thus, the experiment hasC(11,3)=165

equally likely outcomes in its sample space.

What is the probability that at least two 5-dollar bills were drawn, given that no 10-dollar bills were drawn?

Enter your answer as a fraction in lowest terms.

(2 points)

Miley Cyrus has seven background dancers for her performance at the Grammys, five of them are wearing black costumes and two are wearing white costumes. If two of the dancers are selected at random to join Miley Cyrus onstage for the encore, what is the probability that at least one will be wearing black given that at least one is wearing white?

Enter your answer as a fraction in lowest terms.

(2 points)

Ten students, including Lauryn and D'Angelo, sit randomly in a row of ten chairs.

What is the probability that D'Angelo is sitting in the first chair given that Lauryn is not sitting in the second chair?

Enter your answer as a whole number or a fraction in lowest terms.

(2 points)

A box contains seven chocolates -- two with pecans, three with coconut, and two with raspberry creme. Harley Quinn eats three of the chocolates, chosen randomly. If it is known that at least one of the ones she eats has coconut, what's the probability that exactly two of them have coconut?

Enter your answer as a fraction in lowest terms

(4 points)

Paige Turner loves finite mathematics. She has six books about probability and five books about matrices. She lends her friend Anita Tudor four of these books, selected completely randomly.

What is the probability Paige lends Anita two books on each topic (i.e. two matrix books and two probability books), given that she lends her at least one book on each topic?

What is the probability Paige lends Anita four books on probability, given that all the books she lends her are on the same topic?

Enter your answers as fractions in lowest terms.

(2 points)

SupposeA={b,c,d,e,f}

.

A subset ofA

is selected at random -- i.e. all subsets have an equal chance of being selected. If the subset is not empty, what is the probability it contains the elementb?

Enter your answer as a fraction in lowest terms.

(4 points)

An experiment has sample spaceS={a,b,c,d,e}, with all outcomes equally likely.

Consider eventsE={a,c,e} andF={c,d,e}

.

What isPr(E|F)?

What isPr(E|F)?

What isPr(E|F)?

What isPr(E|F)?

Enter each answer as a whole number or a fraction in lowest terms.

(4 points)

A used car lot has 16 Hondas, 2 of which have new tires, 56 Kias, 4 of which have new tires, and 96 Toyotas, 15 of which have new tires. A car from the lot is selected at random. LetH be the event that the car is a Honda,K be the event that the car is a Kia,T be the event that the car is a Toyota, andN be the event that the car has new tires.

What isPr(H|N)?

What isPr(N|H)?

What isPr(K|H)?

What isPr(T|N)?

Enter your answers as whole numbers or fractions in lowest terms.

(3 points)

A diplomatic team consists of six Australians, including Dame Edna, and three New Zealanders, including Stephen Peter Kearney. The team must select two members to serve as officers: one as Spokesperson and another as Chairperson. The officers are selected at random.

What is the probability that Dame Edna is the Chairperson given that Stephen Peter Kearney is the Spokesperson?

What is the probability that Dame Edna is the Chairperson given that Stephen Peter Kearney is not the Spokesperson?

What is the probability that both officers are New Zealanders given that they are both from the same country?

Enter your answers as whole numbers or fractions in lowest terms

(4 points)

A used car lot has 24 Hondas, 4 of which have new tires, 18 Kias, 2 of which have new tires, and 60 Toyotas, 11 of which have new tires. A car from the lot is selected at random. LetH

be the event that the car is a Honda,K

be the event that the car is a Kia,T

be the event that the car is a Toyota, andN

be the event that the car has new tires.

Two eventsE andF areindependentwhenPr(EF)=Pr(E)Pr(F)

.

AreHandKindependent?

A.Yes

B.No

AreHandNindependent?

A.Yes

B.No

AreKandNindependent?

A.Yes

B.No

AreNandTindependent?

A.Yes

B.No

(4 points)

Two ordinary fair, six-sided dice are rolled.

What is the probability the sum of the numbers on the two dice is 6, given that the number on at least one of the dice is 4?

What is the probability the sum of the numbers on the two dice is 8, given that the number on at least one of the dice is 4?

What is the probability the sum of the numbers on the two dice is 7, given that it is not 4?

What is the probability exactly one of the dice shows the number 1 given that the sum of the numbers is 4?

Enter your answers as whole numbers or factions in lowest terms.