Please answer form 6-14

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

1) One possible outcome of this experiment is 5-2 (the first diecomes up 5 and the second die comes up 2). Write out the rest ofthe sample space for this experiment below by completing thepattern:

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

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

3) Draw a circle (or shape) around each of the following events(like you would to circle a word in a word search puzzle). Labeleach event in the sample space with the corresponding letter. EventA has been done for you.

A: Roll a sum of 3.
B: Roll a sum of 7.
C: Roll a sum of at least 10.

D: Roll doubles.
E: Roll snake eyes (two 1’s). F: First die is a 4.

4) Find the following probabilities:
P(A) = _________ P(B) = _________ P(C) = _________

P(D) = _________ P(E) = _________ P(F) = _________

5) The conditional probability of B given A, denoted by P(B|A),is the probability that B will occur when A has already occurred.Use the sample space above (not a special rule) to find thefollowing conditional probabilities:

P(D|C) = _________ P(E|D) = _________ P(D|E) = _________ P(A|B)= _________ P(C|F) = _________

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

Are C and E mutually exclusive? ___________
Find the probability of rolling a sum of at least 10 and snake eyeson the same roll, using the

sample space (not a special rule).
P(C and E) = __________

Find the probability of rolling a sum of at least 10 or snakeeyes, using the sample space. P(C or E) = __________

7) Special case of Addition Rule: If A and B are mutuallyexclusive events, then P(A or B) = P(A) + P(B)

Use this rule to verify your last answer in #6:
P(C or E) = P(C) + P(E) = ________ + ________ = _________

8) Are C and F mutually exclusive? __________ Using samplespace, P(C or F) = _________ 9) Find the probability of rolling a“4” on the first die and getting a sum of 10 or more, using the

sample space.
P (C and F) = ________

10) General case of Addition Rule: P(A or B) = P(A) + P(B) – P(Aand B) Use this rule to verify your last answer in #8:

P(C or F) = P(C) + P(F) – P(C and F) = ________ + ________ ?________ = _________

11) 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 the sample space: P(D|C) =________ . P(D) = ________ .
Are D and C independent? _________
When a gambler rolls at least 10, is she more or less likely toroll doubles than usual? ___________ Compare P(C|F) to P(C), usingthe sample space: P(C|F) = ________ . P(C) = ________ .

Are C and F independent? __________
12) Special case of Multiplication Rule: If A and B areindependent, then P(A and B) = P(A) · P(B).

Use this rule to verify your answer to #9:
P(C and F) = P(C) • P(F) = ________ · ________ = ________ .

13) Find the probability of rolling a sum of at least 10 andgetting doubles, using the sample space. P(C and D) = ________.

14) General case of Multiplication Rule: P(A and B) = P(A) ·P(B|A). Use this rule to verify your answer to #13:

P(C and D) = P(C) • P(D|C) = ________ · ________ = ________.