I. Consider the random experiment of rolling a pair of dice.Note: Write ALL probabilities as reduced fractions or whole numbers(no decimals).

1-1	2-1	3-1	4-1	5-1	6-1
1-2	2-2	3-2	4-2	5-2	6-2
1-3	2-3	3-3	4-3	5-3	6-3
1-4	2-4	3-4	4-4	5-4	6-4
1-5	2-5	3-5	4-5	5-5	6-5
1-6	2-6	3-6	4-6	5-6	6-6

2) How many outcomes does the sample space contain?_____36________

3)Draw a circle (or shape) around each of the following events(like you would circle a word in a word search puzzle). Label eachevent in the sample space with the corresponding letter.

A: Roll a sum of 3.

B: Roll a sum of 6.

C: Roll a sum of at least 9.

D: Roll doubles.

E: Roll snake eyes (two 1’s). F: The first die is a 2.

3) Two events are mutually exclusive if they have no outcomes incommon, so they cannot both occur at the same time.

Are C and F mutually exclusive? ___________

Using the sample space method (not a special rule), find theprobability of rolling a sum of at least 9 and rolling a 2 on thefirst die on the same roll. P(C and F) = __________

Using the sample space method (not a special rule), find theprobability of rolling a sum of at least 9 or rolling a 2 on thefirst die on the same roll.

P(C or F) = __________

4) Special case of Addition Rule: If A and B are mutuallyexclusive events, then

P(A or B) = P(A) + P(B)

Use this rule and your answers from page 1 to verify your lastanswer in #6:

P(C or F) = P(C) + P(F) = ________ + ________ = _________

5) Are D and F mutually exclusive? __________

Using the sample space method, P(D or F) = _________

6) Using the sample space method, find the probability ofrolling doubles and rolling a “2” on the first die.

P (D and F) = _______

7) General case of Addition Rule: P(A or B) = P(A) + P(B) – P(Aand B)

Use this rule and your answers from page 1 and #9 to verify yourlast answer in #8:

P(D or F) = P(D) + P(F) – P(D and F) = ________ + ________ −________ = _________

8) Two events are independent if the occurrence of one does notinfluence the probability of the other occurring. In other words, Aand B are independent if P(A|B) = P(A) or if P(B|A) = P(B).

Compare P(D|C) to P(D), using your answers from page 1: P(D|C) =________ P(D) = ________ Are D and C independent? _________ because_______________________________

When a gambler rolls at least 9, is she more or less likely toroll doubles than usual? ___________ Compare P(D|F) to P(D), usingyour answers from page 1: P(D|F) = ________ P(D) = ________

Are D and F independent? __________ because______________________________

9) Special case of Multiplication Rule: If A and B areindependent, then P(A and B) = P(A) · P(B).

Use this rule and your answers from page 1 to verify your answerto #9: P(D and F) = P(D) • P(F) = ________ · ________ = ________.

10) Find the probability of rolling a sum of at least 9 andgetting doubles, using the sample space method.

P(C and D) = ___________ .

11) General case of Multiplication Rule: P(A and B) = P(A) ·P(B|A).

Use this rule and your answers from page 1 to verify your answerto #13: P(C and D) = P(C) • P(D|C) = ________ · ________ = ________.