Question

Which of the following statements is true?

A. If A and B are independent events then, P (A or B) = P (A) + P (B)
B. If A and B are mutually exclusive events then P (A / B) = 0, as long as P (B) is not equal to 0.
C. If S = {all apartments for rent} and A = {all apartments for rent for less than $ 300 per month} then A '= {all apartments for rent for more than $ 300 per month.

Answer 1

A) False

For independent event P(A and B) =P(A) *P(B)

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

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

B) True

Mutually exclusive events P(A n B)=0

P(A | B) =P( A n B)/P(B) =0

For P(B)=0 ,then only event A occurs.so,it is not possible mutually exclusive events

So,P(B) should not equal to zero.

C) False

S={all apartments for rent}

A={all apartments for rent for less than $300 per month}

A'={all apartments for rent $300 or more than $300 per month}

Here,A' only consider more than $300 per month so,it is wrong.