If Pr(A) =0.5 and Pr(B)=0.5. Which statement about Pr(A∩B) is true?

Question

a) Pr(A∩B) >= 0.3

b) Pr(A∩B) <= 0.3

c) Pr(A∩B) = 0.5

d) None of the options

Answer 1

The intersection of two events must be totally inside both events. Thus Pr(A∩B) must be less than or equal to 0.5 to be inside event A and less than or equal to 0.5 to be inside event B. Since we have no extra information about events A and B, the correct answer is less than or equal to 0.5. That is not one of the options listed. Thus the best answer is D). None of the options.

Answer 2

Are A and B independent variables?