Question

a) Compute the indicated quantity.

P(A | B) = .1, P(B) = .4. Find P(A ∩ B).

P(A ∩ B) =

b)Compute the indicated quantity.

P(A) = .1, P(B) = .2. A and B are independent. Find P(A ∩ B).

P(A ∩ B) =

c)Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. HINT [See Example 1.]

The red one is 1, given that the sum is 7.

Answer 1

a) P(A ∩ B) = P(A | B) * P(B) = 0.1 * 0.4 = 0.04

b) P(A ∩ B) = P(A) * P(B) = 0.1 * 0.2 = 0.02

c) Sample space for sum of 7 = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

sample space for red one is 7 and sum of 7 = {(1,6)}

P(the red one is 1, given that the sum is 7) = P(the red one is 1 and the sum is 7) / P(sum of 7)

                                                                     = (1/36) / (6/36)

                                                                     = 1/6