1.A box is filled with several party favors. It contains 11 hats, 13 noisemakers, ten finger traps, and five bags of confetti.

Let H = the event of getting a hat.

Let N = the event of getting a noisemaker.

Let F = the event of getting a finger trap.

Let C = the event of getting a bag of confetti.

Find P(H). (Enter your probability as a fraction.)

2. A box is filled with several party favors. It contains 16 hats, 18 noisemakers, ten finger traps, and five bags of confetti.

Let H = the event of getting a hat.

Let N = the event of getting a noisemaker.

Let F = the event of getting a finger trap.

Let C = the event of getting a bag of confetti.

Find P(F). (Enter your probability as a fraction.)

3. A jar of 150 jelly beans contains 20 red jelly beans, 38 yellow, 28 green, 26 purple, 24 blue, and the rest are orange.

Let B = the event of getting a blue jelly bean.

Let G = the event of getting a green jelly bean.

Let O = the event of getting an orange jelly bean.

Let P = the event of getting a purple jelly bean.

Let R = the event of getting a red jelly bean.

Let Y = the event of getting a yellow jelly bean.

Find P(Y). (Enter your probability as a fraction.)

4. What is the probability of rolling an odd number of dots with a fair, six-sided die numbered one through six? (Enter your probability as a fraction.)

5. On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters.

Let I = the event that a player is an infielder.

Let O = the event that a player is an outfielder.

Let H = the event that a player is a great hitter.

Let N = the event that a player is not a great hitter.

Write the symbols for the probability that a player is not an outfielder.

a.P(I AND H AND N)

b.P(O|I)

c.P(O') = P(I)

d. P(I OR H OR N)

e. P(I') = P(O)

6.On a baseball team, there are infielders and outfielders. Some players are great hitters, and some players are not great hitters.

Let I = the event that a player is an infielder.

Let O = the event that a player is an outfielder.

Let H = the event that a player is a great hitter.

Let N = the event that a player is not a great hitter.

Write the symbols for the probability that a player is an infielder, given that the player is a great hitter.

a.P(I AND H)

b.P(I OR N)

c.P(I|H')

d.P(I|H)

e. P(O'|N)

7.A shelf holds 12 books. Eight are fiction and the rest are nonfiction. Each is a different book with a unique title. The fiction books are numbered one to eight. The nonfiction books are numbered one to four. Randomly select one book.

LetF= event that book is fiction.

LetN= event that book is nonfiction.

What is the sample space? (Type answer using letter/number combinations separated by commas. Example: F1, N1, ...)

8.EandFare mutually exclusive events.P(E) =0.5;

P(F) =0.2.

FindP(E|F).

(Enter your answer to one decimal place.)

P(E|F) =

9.QandRare independent events.P(Q) =0.2;P(Q AND R) =0.06. FindP(R).

P(R) =

10.An experiment consists of first rolling a die and then tossing a coin.

(a) List the sample space.

a. {(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}

b. {(3, H), (3, T), (4, H), (4, T)}

c. {(1, H), (2, H), (3, H), (4, H), (5, H), (6, H)}

d. {(3, H), (4, H)}

e.{(1, T), (2, T), (3, T), (4, T), (5, T), (6, T)}

(b) LetAbe the event that either a three or a four is rolled first, followed by landing a head on the coin toss. FindP(A).(Enter your probability as a fraction.)

P(A) =

(c) Suppose that a new experiment consists of first rolling a die and then tossing a coin twice. LetBbe the event that the first and second coin tosses land on heads. LetCbe the event that either a three or a four is rolled first, followed by landing a head on the first coin toss. Are the eventsBandCmutually exclusive? Explain your answer.

a. EventsBandCare mutually exclusive because they have different probabilities.

b. EventsBandCare mutually exclusive because the first and second coin tosses cannot land on heads when a three or four is rolled first.

c. EventsBandCare not mutually exclusive because the first and second coin tosses can land on heads when a three or four is rolled first.

d. EventsBandCare mutually exclusive because they are dependent events.