In problem 2 suppose for events A and B we have PA 60 PB 3

In problem 2, suppose for events A and B we have P(A) = .60, P(B) = .30, and P(A or B) = .70. 2.a. Find P(A bar). b. Find P(A intersection B). c. Find P(A intersection B bar). d. Find P(B | A). 3. In parts a - b, suppose A and B are independent events and P(A) = .40, P(B) = .80. a. Find P(A or B) b. Find P(A | B). In parts c - d, suppose A and B are mutually exclusive events with P(A) = .70 and P(B) = .20. c. Find P(A and B bar ). d. Find P(A or B).

Solution

(2)(a) P(Abar) =1-P(A)=1-0.6=0.4

(b) P(A or B) = P(A)+P(B)-P(A and B) =0.7

--> 0.6+0.3-P(A and B) =0.7

So P(A and b) = 0.6+0.3-0.7=0.2

(c) P(A and Bbar) = P(A)-P(A and B)=0.6-0.2 =0.4

(d)P(B|A) = P(A and B)/P(A)= 0.2/0.6 =0.3333

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(3)(a) P(A or B) = P(A)+P(B)-P(A and B)

=0.4+0.8-0.4*0.8 = 0.88

(b) P(A|B) = P(A and B)/P(B) =0.4*0.8 /0.8 =0.4

(c)P(A and Bbar) = P(A)-P(A and B) =0.7

(d) P(A or B) = P(A)+P(B)-P(A and B)

=0.7+0.2-0

=0.9