Question

True or False: (a) Consider two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that P r ( A ∪ B ) = P r ( A ) + P r ( B ) . (b) Consider the two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that P r ( A ∩ B ) = P r ( A ) (c) Consider the two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that A and B are independent.

Answer 1

(a) Consider two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that

P r ( A ∪ B ) = P r ( A ) + P r ( B ) .

given P r ( A ∩ B ) > 0 which says that events A and B are not mutually exclusive

hence P r ( A ∪ B ) = P r ( A ) + P r ( B ) .- P r ( A ∩ B )

Statement is false.

b) Consider the two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that P r ( A ∩ B ) = P r ( A )

If Events A and B are two independent events then the probability P r ( A ∩ B ) > 0 and P r ( A ∩ B )=P r ( A ) * P r ( B ) .

P(A∩B) = P(A)P(B|A) ≤ P(A)

statement is true

(c) Consider the two events A and B such that P r ( A ∩ B ) > 0 . For these events, it is possible that A and B are independent.

If Events A and B are two independent events then the probability P r ( A ∩ B ) > 0 and P r ( A ∩ B )=P r ( A ) * P r ( B ) .

statement is true.