Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

If A and B are two events such that P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`, then P(A) equals ______.

In Question 64 above, P(B|A′) is equal to ______.

If A and B are such events that P(A) > 0 and P(B) ≠ 1, then P(A′|B′) equals ______.

If A and B are two independent events with P(A) = `3/5` and P(B) = `4/9`, then P(A′ ∩ B′) equals ______.

If A and B are two independent events with P(A) = `3/5` and P(B) = `4/9`, then P(A′ ∩ B′) equals ______.

If two events are independent, then ______.

Let A and B be two events such that P(A) = `3/8`, P(B) = `5/8` and P(A ∪ B) = `3/4`. Then P(A|B).P(A′|B) is equal to ______.

If the events A and B are independent, then P(A ∩ B) is equal to ______.

Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E|F) – P(F|E) equals ______.

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

If A and B are independent events, then A′ and B′ are also independent

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

Two independent events are always mutually exclusive.

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

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

If A and B are independent, then P(exactly one of A, B occurs) = P(A)P(B') + P(B)P(A') 

If A and B are two events such that P(A) > 0 and P(A) + P(B) >1, then P(B|A) ≥ `1 - ("P"("B'"))/("P"("A"))`

If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then P(At least two of A, B, C occur) = 3p² – 2p³ 

If A and B are two events such that P(A|B) = p, P(A) = p, P(B) = `1/3` and P(A ∪ B) = `5/9`, then p = ______.

Let A and B be two events. If P(A | B) = P(A), then A is ______ of B.