Q. 55.0( 2 Votes )

# If A and B be two events such that P(A) = 1/4, P (B) = 1/3 and P (A ∪ B) = 1/2, show that A and B are independent events.

Answer :

P (A ∪ B)=P(A)+P(B)–P(A∩B)

Therefore A and B are independent events.

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If A and B are two independent events such that P(A’ ∩ B) = 2/15 and P(A ∩ B’) = 1/6 then find P(A) and P(B).

Mathematics - Board PapersState True or False for the statements in the Exercise.

If A and B are two independent events then P(A and B) = P(A).P(B)

Mathematics - ExemplarState True or False for the statements in the Exercise.

If A and B are mutually exclusive events, then they will be independent also.

Mathematics - ExemplarState True or False for the statements in the Exercise.

If A and B are independent, then

P (exactly one of A, B occurs) = P(A)P(B′)+P(B) P(A′)

Mathematics - ExemplarState True or False for the statements in the Exercise.

If A and B are independent events, then P(A′ ∪ B) = 1 – P (A) P(B′)

Mathematics - ExemplarState True or False for the statements in the Exercise.

Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.

Mathematics - ExemplarProve that if E and F are independent events, then the events E and F are also independent.

Mathematics - Board Papers