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.
(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.
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