Question

Rework problem 4 from section 3.1 of your textbook, about events A and B of a sample space S, but assume that Pr[A]=0.15 and Pr[B]=0.35. Find Pr[A∪B] under each of the following conditions: (1) If A⊂B, then Pr[A∪B]= equation editorEquation Editor . (2) If A∩B=∅, then Pr[A∪B]= equation editorEquation Editor . (3) If A∩B′=∅, then Pr[A∪B]= equation editorEquation Editor .

Answer 1

1) If A B, then P(A B) = P(B) = 0.35.

2) If, A B = then, P(A B) = 0

Thus, P(A B) = P(A) + P(B) - P(A B) = 0.15 + 0.35 - 0 = 0.50.

3) If A B' = , then P(A B') = 0

Now, P(A) = P(A B) + P(A B') i.e. P(A) = P(A B)

Thus, P(A B) = P(A) + P(B) - P(A B) = 0.15 + 0.35 - 0.15 = 0.35.