Question

1. Use the following table for the 2 dice problem.

Note: An “AB” is both an “A” and a “B” at the same time

1st roll / 2nd roll — в А в в А Т АВ AB

1. What is P(A) = #A’s/36?
2. What is P(B) = #B’s/36?
3. What is P(A ∩ B) = #AB’s/36?
4. What is P(B|A) = #AB’s/#A’s?
5. What is P(A|B) = #AB’s/#B’s?
6. Are events A and B mutually exclusive? (yes or no) Be sure to give your reasoning.
7. Are events A and B mathematically independent? (yes or no) Be sure to give your reasonin Hint: Compute P(A)*P(B), and P(A∩B) and compare.

Answer 1

(a) P(A) = 12/36 = 1/3

(b) P(B) = 6/36 = 1/6

(c) P(AB) = 2/36 = 1/18

(d) P(B|A) = 2/12 = 1/6

(e) P(A|B) = 2/6 = 1/3

(f) A and B are not mutually exclusive as twice A and B occur together in twice this cases and hence P(A U B) not equal to P(A) + P(B)

(g) SInce P(A $\bigcap$ B) = P(A) * P(B), hence they are mathematically independent.