Answer to Question #210126 in Electrical Engineering for Bahawal Tahir

Question

Q

Two events A and B are such that P(A) =2. P(B) =.3, aud P(A U B) =4. Find the following:

a. P(A intersection B)

b. P(A' U B')

c. P(A' intersection B')

d. P(A' |B)

Answer 1

P(AUB) = P(A)+P(B) - P(A intersect B) =

a.) P(AUB) = 2+0.3 - 4= -1.7

b) P(A|(AUB)) = P(A intersect (AUB))/P(AUB) = P(A)/P(AUB) (Because A intersect (A U B) is A)

= 2/-1.7 = 2/-1.7

c) P(A|A intersection B) = P(A intersection (A intersection B))/P(A intersect B) =

P(A intersect B)/P(A intersect B) = 4/4 = 1

d) (A intersect B|AUB) = P((A intersect B)intersect (AUB))/P(AUB) = P(A intersect B)/P(A UB) = 0.3/-1.7 = 0.1765 because the A intersect B falls with A U B and the only values they have in common/intersect are the A intersect B ones.