Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Determine P(E|F).

Mother, father and son line up at random for a family picture

E: son on one end, F: father in middle

A black and a red dice are rolled. 

Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

A black and a red dice are rolled. 

Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|F) and P (F|E)

A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|G) and P (G|E)

A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P ((E ∪ F)|G) and P ((E ∩ G)|G)

An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple-choice question?

Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.

If P(A) = `1/2`,  P(B) = 0, then P(A|B) is ______.

A die is tossed thrice. Find the probability of getting an odd number at least once.

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that

1. both balls are red.
2. first ball is black and second is red.
3. one of them is black and other is red.

A and B are two events such that P (A) ≠ 0. Find P (B|A), if  A is a subset of B.

A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.

If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?

In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.

Suppose we have four boxes. A, B, C and D containing coloured marbles as given below:

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?

A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

Find the direction cosines of a line which makes equal angles with the coordinate axes.

If a line has the direction ratios −18, 12, −4, then what are its direction cosines?