1- A sample space consists of five simple events with

P(E₁) = P(E₂) = 0.3, P(E₃) = 0.1, P(E₄) = 0.2, and P(E₅) = 0.1.

Find the probability of the event

A = {E₁, E₃, E₄}.

P(A) =

2-A sample space consists of five simple events with

P(E₁) = P(E₂) = 0.25, P(E₃) = 0.2, and P(E₄) = 2P(E₅).

Find the probability of the event

B = {E₂, E₃}.

P(B) =

3- A single card is randomly drawn from a deck of 52 cards.List the simple events in the sample space.

Assign probabilities to the simple events. (Enter your probability as a fraction.)Since any card as just as likely as any other, each event in the sample space has a probability of .Find the probability that the card is a king. (Enter your probability as a fraction.)

4- A sample space contains seven simple events:

E₁,E₂,,E₇.

Suppose that

E₁,E₂,,E₆

all have the same probability, but

E₇

is four times as likely as the others. Find the probability of the given event.

B=

E₁,E₃,E₄,E₇

5- Three children are selected, and their gender recorded. Assume that males and females are equally likely.List the simple events in the sample space. (Enter your answer as a comma-separated list. Enter each simple event in the format (G₁, G₂, G₃) where G_i is the gender of the ith child. Use M for male and F for female.)

Assign probabilities to the simple events. (Enter your probability as a fraction.)Each event is equally likely, with probability .What is the probability that there are two girls and one boy in the group? (Enter your probability as a fraction.)

6- A bowl contains four candiesred, brown, yellow, and green. Draw two candies at random, one for you to eat, and one for a friend. (Assume you eat the first candy drawn.)List the simple events in the sample space. (Enter your answers as a comma-separated list. Enter each simple event in the format (C₁, C₂) where C_i is the color of the ith candy. Use R for red, B for brown, Y for yellow, and G for green.)

Assign probabilities to the simple events. (Enter your probability as a fraction.)Each event is equally likely, with probability .What is the probability that you get the brown candy and your friend does not get the red one? (Enter your probability as a fraction.)

7- A single fair six-sided die is tossed. Assign probabilities to the simple events and calculate the given probability. (Enter your probability as a fraction.)B: observe an odd numberP(B) =

8- A single fair six-sided die is tossed. Assign probabilities to the simple events and calculate the given probability. (Enter your probability as a fraction.)C: observe a number greater than 3P(C) =

9- A sample space consists of five simple events with

P(E₁) = P(E₂) = 0.2, P(E₃) = 0.3, P(E₄) = 0.2, and P(E₅) = 0.1.

Consider the following event A.

A = {E₁, E₃, E₄}

Find the probability that event A does not occur.P(not A) =

10- A sample space contains seven simple events:

E₁,E₂,,E₇.

Suppose that

E₁,E₂,,E₆

all have the same probability, but

E₇

is four times as likely as the others. Find the probability of the given event.

C=

E₄,E₅

11- A sample space consists of five simple events with

P(E₁) = P(E₂) = 0.15, P(E₃) = 0.55, and P(E₄) = 2P(E₅).

Find the probabilities for simple events E₄ and E₅.

P(E₄)

=

P(E₅)

=

12- A single fair six-sided die is tossed. Assign probabilities to the simple events and calculate the given probability. (Enter your probability as a fraction.)A: observe a 3P(A) =

13- A single card is randomly drawn from a deck of 52 cards.Find the probability that it is a number less than 7 (not including the ace). (Enter your probability as a fraction.)

14- A sample space consists of five simple events with

P(E₁) = P(E₂) = 0.25, P(E₃) = 0.35, P(E₄) = 0.1, and P(E₅) = 0.05.

Consider the following events A and B.

A	=	{E1, E3, E4}
B	=	{E2, E3}

Find the probability of either A or B or both.P(either A or B or both) =

15- A bowl contains four candiesred, brown, yellow, and green. Draw two candies at random, one for you to eat, and one for a friend. (Assume you eat the first candy drawn.)What is the probability that you get either yellow or green and your friend gets either brown or red?

16- Use the mn Rule to find the number of items in the following exercise.There are three groups of distinctly different items, six in the first group, eight in the second, and two in the third. If you select one item from each group, how many different triplets can you form? triplets

17- Evaluate the permutation.

P

12

11

18- Evaluate the permutation.

P

50

1

19- Use the mn rule to find the number of items.There are two groups of distinctly different items, 20 in the first group and 6 in the second. If you select one item from each group, how many different pairs can you form? pairs

20- Evaluate the permutation.

P

6

4

21- Use the mn Rule to find the number of items in the following exercise.Five coins are tossed. How many simple events are in the sample space? simple events

22- Evaluate the combination.

C

9

7

23- Use the mn Rule to find the number of items in the following exercise.Five dice are tossed. How many simple events are in the sample space? simple events

24- Evaluate the combination.

C

9

8

25- Evaluate the permutation.

P

7

7