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

For a loaded die, the probabilities of outcomes are given as under:
P(1) = P(2) = 0.2, P(3) = P(5) = P(6) = 0.1 and P(4) = 0.3. The die is thrown two times. Let A and B be the events, ‘same number each time’, and ‘a total score is 10 or more’, respectively. Determine whether or not A and B are independent.

Refer to Question 1 above. If the die were fair, determine whether or not the events A and B are independent.

The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate `"P"(bar"A") + "P"(bar"B")`

Two dice are thrown together and the total score is noted. The events E, F and G are ‘a total of 4’, ‘a total of 9 or more’, and ‘a total divisible by 5’, respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are independent.

A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`. Find: `"P"("A"/"B")`

A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`. Find: `"P"("B"/"A")`

A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`. Find: `"P"("A'"/"B")`

A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`. Find: `"P"("A'"/"B'")`

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 ______.