Question

1) a. If A and B are two events, in general, P( A U B) =...

1) a. If A and B are two events, in general, P( A U B) =

b. if A and B are two mutually exclusive events, P( A U B)=

c. If A and B are two events, in general P( A ∩ B)=

d. If A and B are two independent events, P(A ∩ B)= , since A and B being independent means ___________

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Homework Answers

Answer #1

1)

a. If A and B are two events, in general, P( A U B) = P(A) + P(B) – P(A ∩ B)

(by using definition of union of two events in general.)

b. if A and B are two mutually exclusive events, P( A U B)= P(A) + P(B)

Explanation:

For two mutually exclusive events A and B, we know that P(A ∩ B) = 0, so

P( A U B) = P(A) + P(B) – P(A ∩ B) = P(A) + P(B) – 0 = P(A) + P(B)

c. If A and B are two events, in general P( A ∩ B) = P(A) + P(B) – P(A U B)

(by using definition of union and intersection of two events in general)

d. If A and B are two independent events, P(A ∩ B)= P(A)*P(B), since A and B being independent means

(by using definition of intersection of two independent events A and B)

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