Probability: Class 12 Previous Year Questions

Probability questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. Check whether the lines given by x – 1 2 = y – 2 3 = z – 3 4 and x – 4 5 = y – 1 2 = z are parallel or not. If parallel, find the distance between them, otherwise find their point of intersection, if the lines are intersecting.
   Board 20265 markslong answer
2. { } 37. In an online jackpot, there is one first prize of ` 3,00,000, two second prizes of ` 2,00,000 each and three third prizes of ` 50,000 each. A total of 1,00,000 jackpot tickets each costing ` 100 were sold there by raising a fund of ` 1,00,00,000. Rohan…
   Board 20264 marksshort answer
3. (a) Out of two bags, bag I contains 3 red and 4 white balls and bag II contains 8 red and 6 white balls. A die is thrown. If it shows a number less than 3 then a ball is drawn at random from bag I, otherwise a ball is drawn at random from bag II. Find the prob…
   Board 20263 marksshort answer
4. (a) The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. 3 The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the pr…
   Board 20263 marksshort answer
5. { } 19. Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is 2 3 . 1 Reason (R) : For any two events A and B, P(A|B) = P(A  B) P(B) 12 { } 20.  (A) : …
   Board 20261 markAssertion-Reason
6. P(F) : If E and F are two independent events such that P(E) = 7. then P(E/F) is equal to : 1- (A) (B) 2-3 (C) (D) Page 5 of 24 8. : [] g = () (A) (B) (C) (D) -1 -2 [-2] B= 9. = V · -1 -5 [9 L-3 L-7 AB (A) (B) AC BA (C) (D) AB, AC BA 10. -1 (A) (B) -log 2 log 2…
   Board 20251 markMCQ
7. A bank offers loan to its customers on different types of interest namely, fixed rate, floating rate and variable rate. From the past data with the bank, it is known that a customer avails loan on fixed rate, floating rate or variable rate with probabilities 1…
   Board 20254 marksshort answer
8. Three persons viz. Amber, Bonzi and Comet are manufacturing cars which run on petrol and on battery as well. Their production share in the market is 60%, 30% and 10% respectively. Of their respective production capacities, 20%, 10% and 5% cars respectively are…
   Board 20254 marksshort answer
9. (a) The probability distribution for the number of students being absent in a class on a Saturday is as follows : P(X) 2p 3p Where X is the number of students absent. (i) Calculate p. (i) Calculate the mean of the number of absent students on Saturday. OR (b) …
   Board 20253 marksshort answer
10. (a) A die with number 1 to 6 is biased such that P(2) : and probability of 10 other numbers is equal. Find the mean of the number of times number 2 appears on the dice, if the dice is thrown twice. OR (b) Two dice are thrown. Defined are the following two even…
    Board 20253 marksshort answer
11. Page 21 of 23 37. According to recent research, air turbulence has increased in various regions around the world due to climate change. Turbulence makes flights bumpy and often delays the flights. Assume that, an airplane observes severe turbulence, moderate t…
    Board 20244 marksshort answer
12. (a) The probability distribution of a random variable X is given below : X 1 2 3 P(X) 2 k 3 k 6 k (i) Find the value of k. (ii) Find P(1 X < 3). (iii) Find E(X), the mean of X. OR (b) A and B are independent events such that P(A B ) = 4 1 and P( A B) = 6 1 . F…
    Board 20233 marksshort answer
13. If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is : (A) (B) (C) (D) 18 tan x
    Board 20231 markMCQ
14. (a) Two balls are drawn at random one by one with replacement from an urn containing equal number of red balls and green balls. Find the probability distribution of number of red balls. Also, find the mean of the random variable. OR (b) A and B throw a die alt…
    Board 20233 marksshort answer
15. JJJJ Page 19 36. There are different types of Yoga which involve the usage of different poses of Yoga Asanas, Meditation and Pranayam as shown in the figure below : Types of Yoga Hatha Yoga Bikram Yoga Vinyasa Yoga Kundalini Yoga Anusara Yoga JJJJ Page 20 ZrMo…
    Board 20234 marksshort answer
16. Recent studies suggest that roughly 12% of the world population is left handed. Page 20 76% 24,CHANCEOFAL FTHANDEDCHILD 83% 914 ROUGHLY12°OFTHEWORLDISLEFTHANDED 9*,CHANCEOF A LEFT HANDEDCHILD Depending upon the parents, the chances of having a left handed chil…
    Board 20234 marksshort answer
17. Two balls are drawn at random from a bag containing 2 red balls and 3 blue balls, without replacement. Let the variable X denotes the number of red balls. Find the probability distribution of X.
    Board 20221 markvery short
18. nmgm| Ho$ EH$ `w½_ H$mo CN>mbm J`m & XmoZm| nmgm| na AmB© g§»`mAm| H$m `moJ\$b EH$ g_ g§»`m h¡ & H$_-go-H$_ EH$ nmgo na g§»`m 3 AmZo H$s àm{`H$Vm kmV H$s{OE & 2
    Board 20221 markvery short
19. A card from a pack of 52 playing cards is lost. From the remaining cards, 2 cards are drawn at random without replacement, and are found to be both aces. Find the probability that lost card being an ace.
    Board 20221 markvery short
20. 𝐴 and 𝐵 are two independent events such that 𝑃(𝐴) = 1 6 , 𝑃(𝐵) = 𝑘. If the probability of occurrence of exactly one of them is 1 3, then find the value of 𝑘. (A) 1 4 (B) 2 3 (C) 3 4 (D) 5 6 1 *There is no change in the Question Paper Design and Assessment Patt…
    Sample paper 2026-271 markAssertion-Reason

Practise all 34 Probability questions with answers →

Other Class 12 Maths chapters

Frequently asked questions