Fill in the following table when using 2 dice. a. Let event A be that the 1 st d

Question

Fill in the following table when using 2 dice.

a. Let event A be that the 1st die roll is even (2, 4, or 6). Put an A in the appropriate boxes. It does not matter what the 2nd die roll is for event A.

b. Let event B be the sum of both dice equals 5. Put a B in the appropriate boxes.

c. What is P(A)?

d. What is P(B)?

e. What is P(A B)?

f. What is P(B|A)?

g. What is P(A|B)?

h. Are events A and B mutually exclusive? (yes or no) Be sure to give your reasoning.

i. Are events A and B independent? (yes or no) Be sure to give your reasoning. Hint: Compute P(A), P(B), and P(AB) and compare.

6 5 4 3 2 1123456

Explanation / Answer

(c) There are 18 boxes with A, Hence P(A) = 18/36 = 1/2 = 0.5

(d) There are 4 boxes with B, P(B) = 4/36 = 1/9 = 0.111

(e) There are 2 boxes with A and B, P(A and B) = 2/36 = 0.0556

(f) P(B|A) = P(A and B) / P(A) = 2/18 = 1/9 = 0.1111

(g) P(A|B) = P(A and B) / P(B) = 2/4 = 1/2 = 0.5

(h) As P(A and B) is not equal to zero, events A and B are not mutually exclusive

(i) As P(A and B) = P(A)*P(B), events A and B are independent events

1st roll/2nd Roll 1 2 3 4 5 6 1 B 2 A A A, B A A A 3 B 4 A, B A A A A A 5 6 A A A A A A

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