CBSE Class 12th Mathematics Chapter 13 - Probability Important Questions with Answers
You should focus on solving CBSE Class 12th Mathematics Chapter 13: Probability important questions, especially to help you score high marks. By solving CBSE Class 12th Mathematics 13 questions, you will be solving exam-oriented questions only.
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CBSE Class 12th Mathematics Chapter 13 - Probability Important Questions with Answers are provided in this article to help you score incredible marks. The Council will conduct the CBSE Class 12 Mathematics exam 2025 on March 8, 2025. Before appearing for the exam, you check out all the below mentioned important questions from Chapter 13 of CBSE Board 12th Mathematics syllabus 2025.
Probability, chapter 13 of NCERT focuses on the concept of how likely events are to take place, covering topics like calculating the likelihood of events occurring, conditional probability, independent events, and the multiplication rule of probability. This chapter is usually based on the NCERT syllabus for Class 12 mathematics. Probability delves deeper into the probability theory, that goes beyond basic calculations to explore more complex scenarios involving conditional probabilities and dependent events. Key topics that you must take into consideration are sample space, events, axiomatic approach to probability, conditional probability, Bayes' theorem, multiplication rule, and independent events, Random variable and its probability distribution, mean of random variable.
The CBSE Class 12 Math syllabus 2024-25 is consist of 6 units and 13 chapters in total. The CBSE 12th Math exam 2025 is going to be conducted for 80 marks, and the remaining 20 marks will be evaluated on project. The CBSE 12th Math project will include periodic tests
and mathematics activities. The Math syllabus does not have chapter-wise division of marks. Instead, the weightage is based on the competencies which the questions from the chapters will evaluate. Pribability is the chapter 13 of CBSE Class 12 Board Math syllabus 2025 which will have 30 periods and will carry 8 marks in total. Prepare thoroughly with the most important questions of CBSE Class 12th Mathematics Chapter 13 - Probability. You can first cover the CBSE Class 12th Mathematics syllabus to understand the key topics and then start solving the CBSE Class 12th Mathematics Chapter 13 - Probability Important Question to get a better understanding of your preparation level. Start practicing now.
If P(not A) = 0.7, P(B) = 0.7 and P(B/A) = 0.5, then find P(A/B). (All India 2019)
Question 2.
A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event ‘number is even’ and B be the event ‘number is marked red’. Find whether the events A and B are independent or not. (Delhi 2019)
Or
A die, whose faces are marked 1,2, 3 in red and 4, 5, 6 in green , is tossed. Let A be the event “number obtained is even” and B be the event “number obtained is red”. Find if A and B are independent events. (All India 2017)
Question 3.
Find the probability distribution of X, the number of heads in a simultaneous toss of two coins. (All India 2019)
Question 4.
The random variable X has a probability distribution P(X) of the following form, where ‘k’ is some number.
Determine the value of ‘k’. (Delhi 2019)
Question 5.
Suppose a girl throws a the. If she gets 1 or 2, she tosses a coin three times and notes the number of tails. If she gets 3, 4, 5 or 6, she tosses a coin once and notes whether a ‘head’ or ‘tail’ is obtained. If she obtained exactly one ‘tail’, what is the probability that she threw 3, 4, 5 or 6 with the die? (C8SE 2019)
Question 6.
There are three coins. One is two-headed coin, another is biased coin that comes up heads 75% of the time and the third is an unbiased coin. One of three coins is chosen at random and tossed. If it shows heads, what is the probability that it is the two-headed coin? (All India 2019)
Question 7.
A bag contains 5 red and 4 black balls, a second bag contains 3 red and 6 black balls. One of the two bags is selected at random and two balls are drawn at random (without replacement) both of which are found to be red. Find the probability that the balls are drawn from the second bag. (All India 2019)
Question 8.
A manufacturer has three machine operators A, B and C. The first operator A produces 1% of defective items, whereas the other two operators B and C produces 5% and 7% defective items respectively. A is on the job for 50% of the time, B on the job 30% of the time and C on the job for 20% of the time. All the items are put into one stockpile and then one items is chosen at random from this and is found to be defective. What is the probability that it was produced by A? (Delhi 2019)
Question 9.
Two cards are drawn simultaneously (or successively without replacement) from a well-shuffled pack of 52 cards. Find the mean and variance of the number of kings. (Delhi 2019)
Question 10.
A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4. (CBSE 2018)
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Question 1.
Evaluate P(A ? B), if 2P (A) = P(B) = \(\frac{5}{13}\) and P(A/ B) = \(\frac{2}{5}\). (CBSE 2018C)
Question 2.
Two numbers are selected at random (without replacement) from the first five positive integers. Let X denotes the larger of the two numbers obtained. Find the mean and variance of X. (CBSE 2018)
Question 3.
Two groups are competing for the positions of the Board of Directors of a corporation. The probabilities that the first and second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced way by the second group. (CBSE 2018C)
Question 4.
Prove that if E and F are independent events, then the events E and F’ are also independent. (Delhi 2017)
Question 5.
The random variable X can take only the values 0, 1, 2, 3. Given that
P(X = 0) = P(X = 1) = p and
P(X = 2) = P (X = 3) such that
?pixi2 = 2?pixi, find the value of P. (Delhi 2017)
Question 6.
There are 4 cards numbered 1, 3, 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X. (All India 2017)
Question 7.
A and B throw a pair of dice alternately. A wins the game, if he gets a total of 7 and B wins the game, if he gets a total of 10. If A starts the game, then find the probability that B wins. (Delhi 2016)
Question 8.
A and B throw a pair of dice alternately, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first. (All India 2016)
Question 9.
Three persons A, B and C apply for a job of Manager in a private company. Chances of their selection (A, B and C) are in the ratio 1:2:4. The probabilities that A, B and C can introduce changes to improve profits of the company are 0.8, 0.5 and 0.3, respectively. If the change does not take place, find the probability that it is due to the appointment of C. (Delhi 2016)
Question 10.
A bag X contains 4 white balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag Y. (All India 2016)
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Other CBSE Class 12th Mathematics Chapter Wise Questions
