Question

1. Bowl A contains three red and two white chips, and bowl B contains four red and three white chips. A chip is drawn at random from bowl A and transferred to bowl B. Compute the probability of then drawing a red chip from bowl B.

2. Let P(A)=0.3P(A)=0.3 and P(B)=0.6P(B)=0.6. Find P(A∪B)P(A∪B) when AA and BB are indepdenent.

3. Let P(A)=0.3P(A)=0.3 and P(B)=0.6P(B)=0.6. Find P(A|B)P(A|B) when AA and BB are mutually exclusive.

Answer 1

Let P(A) = 0.3 and P(B)= 0.6

when A and B are independent P(A∩ B) = P(A) * P(B)

     P(AUB) = P(A) + P(B) -P(A∩ B)

                  = P(A) + P(B) - P(A) * P(B)

                   =0.3 + 0.6 - 0.3 * 0.6

                  = 0.72

when A and B are mutually exclusive their intersection P(A∩B) is zero.

P(A l B)= P(A∩B)/P(B) = 0/0.6 = 0