Question

1. Two distinguishable (so order matters) fair dice are rolled. Define the following events: A = {sum of the numbers rolled is odd}, B = {sum of the numbers rolled is greater than 8}. (a) Find the probabilities P(A) and P(B). [Hint: First define events A and B explicitly, as a list of all outcomes in an event.] (b) Find the probabilities P(A ? B) and P(A ? B). [Hint: First define events A ? B and A ? B explicitly, as a list of all outcomes in an event.] (c) Are events A and B independent? Why? 2. (6 points) Two marbles are drawn at random without replacement from a box containing 2 red, 3 green, and 4 blue marbles. Let's define the following events: A = {two red marbles are drawn}, B = {two green marbles are drawn}, C = {two blue marbles are drawn}, D = {two marbles of the same color are drawn}. Find each of the following probabilities: P(A), P(B), P(C), P(D), and P(A|D). 3. (6 points) Two marbles are drawn at random with replacement from a box containing 2 red, 3 green, and 4 blue marbles. Let's define the following events: A = {two red marbles are drawn}, B = {two green marbles are drawn}, C = {two blue marbles are drawn}, D = {two marbles of the same color are drawn}. Find each of the following probabilities: P(A), P(B), P(C), P(D), and P(A|D).

          1. Two distinguishable (so order matters) fair dice are rolled. Define the following events:

A = {sum of the numbers rolled is odd},
B = {sum of the numbers rolled is greater than 8}.

(a) Find the probabilities P(A) and P(B). [Hint: First define events A and B explicitly, as a list of all outcomes in an event.]
(b) Find the probabilities P(A ? B) and P(A ? B). [Hint: First define events A ? B and A ? B explicitly, as a list of all outcomes in an event.]
(c) Are events A and B independent? Why?

2. (6 points) Two marbles are drawn at random without replacement from a box containing 2 red, 3 green, and 4 blue marbles. Let's define the following events:

A = {two red marbles are drawn},
B = {two green marbles are drawn},
C = {two blue marbles are drawn},
D = {two marbles of the same color are drawn}.

Find each of the following probabilities: P(A), P(B), P(C), P(D), and P(A|D).

3. (6 points) Two marbles are drawn at random with replacement from a box containing 2 red, 3 green, and 4 blue marbles. Let's define the following events:

A = {two red marbles are drawn},
B = {two green marbles are drawn},
C = {two blue marbles are drawn},
D = {two marbles of the same color are drawn}.

Find each of the following probabilities: P(A), P(B), P(C), P(D), and P(A|D).

1. Two distinguishable (so order matters) fair dice are rolled. Define the following events:

A = sum of the numbers rolled is odd,
B = sum of the numbers rolled is greater than 8.

(a) Find the probabilities P(A) and P(B). [Hint: First define events A and B explicitly, as a list of all outcomes in an event.]
(b) Find the probabilities P(A ? B) and P(A ? B). [Hint: First define events A ? B and A ? B explicitly, as a list of all outcomes in an event.]
(c) Are events A and B independent? Why?

2. (6 points) Two marbles are drawn at random without replacement from a box containing 2 red, 3 green, and 4 blue marbles. Let's define the following events:

A = two red marbles are drawn,
B = two green marbles are drawn,
C = two blue marbles are drawn,
D = two marbles of the same color are drawn.

Find each of the following probabilities: P(A), P(B), P(C), P(D), and P(A|D).

3. (6 points) Two marbles are drawn at random with replacement from a box containing 2 red, 3 green, and 4 blue marbles. Let's define the following events:

A = two red marbles are drawn,
B = two green marbles are drawn,
C = two blue marbles are drawn,
D = two marbles of the same color are drawn.

Find each of the following probabilities: P(A), P(B), P(C), P(D), and P(A|D).

Added by Jeffery C.

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