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

Three events A, B and C have probabilities `2/5, 1/3` and `1/2`, , respectively. Given that P(A ∩ C) = `1/5` and P(B ∩ C) = `1/4`, find the values of P(C|B) and P(A' ∩ C').

Let E₁ and E₂ be two independent events such that P(E₁) = P₁ and P(E₂) = P₂. Describe in words of the events whose probabilities are: P₁P₂ 

Let E₁ and E₂ be two independent events such that P(E₁) = P₁ and P(E₂) = P₂. Describe in words of the events whose probabilities are: (1 – P₁) P₂ 

Let E₁ and E₂ be two independent events such that P(E₁) = P₁ and P(E₂) = P₂. Describe in words of the events whose probabilities are: 1 – (1 – P₁)(1 – P₂) 

Let E₁ and E₂ be two independent events such that P(E₁) = P₁ and P(E₂) = P₂. Describe in words of the events whose probabilities are: P₁ + P₂ – 2P₁P₂ 

Two dice are tossed. Find whether the following two events A and B are independent: A = {(x, y): x + y = 11} B = {(x, y): x ≠ 5} where (x, y) denotes a typical sample point.

If A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`, P(A' ∩ B') equals ______.

If A and B are two events and A ≠ Φ, B ≠ Φ, then ______.

A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5. Then P(B′ ∩ A) equals ______.

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