Probability

179 CBSE Class 12 Mathematics past-year questions from 5 papers, 2022 to 2026, with answers and worked solutions.

Difficulty: 43 easy · 118 moderate · 18 hard.
Most-asked subtopics: Conditional Probability (54), Random Variables and Probability Distributions (36), Independent Events (34).
Updated 19 August 2026.

Filter all 179 in the question bank

#1Conditional Probability
#2Conditional Probability
#3Conditional Probability
#4Conditional Probability
#5Conditional Probability
At the start of a cricket match, a coin is tossed and the team winning the toss has the opportunity to choose to bat or bowl. Such a coin is unbiased with equal probabilities of getting head and tail. Based on the above information, answer the following questions :
Done a few? Here’s your next move
- Filter all 179 by year or level
#6Conditional Probability
#7Conditional Probability
#8Conditional Probability
#9Conditional Probability
There are three types of vaccines $A_1$ , $A_2$ , $A_3$ , available in the market to protect the population of the country from spread of certain infection. According to a survey conducted, it was found that 25% of the population was given Vaccine $A_1$ , 35% of the population was given Vaccine $A_2$ and 40% of the population was given Vaccine $A_3$ . The survey also stated that the probabilities that Vaccines $A_1$ , $A_2$ and $A_3$ would protect against the infection were 60%, 55% and 50% respectively. Based on the above information, answer the following questions : Find the probability that :
#10Conditional Probability
A survey was conducted to find out the success rate of students who qualified the entrance examination by dropping a year after class XII. As per the data collected, 40% students appearing in the examination were dropouts and the remaining students were regular students of class XII. Of the dropouts, 5% qualify the examination while 10% of the regular students qualify the examination. Based on the above information, answer the following questions.
#11Conditional Probability
A survey was conducted to find out the success rate of students who qualified the entrance examination by dropping a year after class XII. As per the data collected, 40% students appearing in the examination were dropouts and the remaining students were regular students of class XII. Of the dropouts, 5% qualify the examination while 10% of the regular students qualify the examination. Based on the above information, answer the following questions.
#12Conditional Probability
#13Conditional Probability
#14Conditional Probability
Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information, answer the following questions :
#15Conditional Probability
Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information, answer the following questions :
#16Conditional Probability
Direction : Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
#17Conditional Probability
#18Conditional Probability
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 bought one ticket. Based on given information, answer the following questions :
#19Conditional Probability
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 bought one ticket. Based on given information, answer the following questions :
#20Conditional Probability
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 bought one ticket. Based on given information, answer the following questions :
#21Conditional Probability
#22Conditional Probability
#23Conditional Probability
#24Conditional Probability
#25Conditional Probability
A departmental store sends bills to charge its customers once a month. Past experience shows that 70% of its customers pay their first month bill in time. The store also found that the customer who pays the bill in time has the probability of 0.8 of paying in time next month and the customer who doesn't pay in time has the probability of 0.4 of paying in time the next month. Based on the above information, answer the following questions :
#26Conditional Probability
A departmental store sends bills to charge its customers once a month. Past experience shows that 70% of its customers pay their first month bill in time. The store also found that the customer who pays the bill in time has the probability of 0.8 of paying in time next month and the customer who doesn't pay in time has the probability of 0.4 of paying in time the next month. Based on the above information, answer the following questions :
#27Conditional Probability
#28Conditional Probability
Rohit, Jaspreet and Alia appeared for an interview for three vacancies in the same post. The probability of Rohit's selection is $\dfrac{1}{5}$ , Jaspreet's selection is $\dfrac{1}{3}$ and Alia's selection is $\dfrac{1}{4}$ . The event of selection is independent of each other. Based on the above information, answer the following questions :
#29Conditional Probability
#30Conditional Probability
#31Conditional Probability
Airplanes are by far the safest mode of transportation when the number of transported passengers are measured against personal injuries and fatality totals. Previous records state that the probability of an airplane crash is $0{\cdot}00001\%$ . Further, there are 95% chances that there will be survivors after a plane crash. Assume that in case of no crash, all travellers survive. Let $E_1$ be the event that there is a plane crash and $E_2$ be the event that there is no crash. Let A be the event that passengers survive after the journey. On the basis of the above information, answer the following questions :
#32Conditional Probability
Airplanes are by far the safest mode of transportation when the number of transported passengers are measured against personal injuries and fatality totals. Previous records state that the probability of an airplane crash is $0{\cdot}00001\%$ . Further, there are 95% chances that there will be survivors after a plane crash. Assume that in case of no crash, all travellers survive. Let $E_1$ be the event that there is a plane crash and $E_2$ be the event that there is no crash. Let A be the event that passengers survive after the journey. On the basis of the above information, answer the following questions :
#33Conditional Probability
#34Conditional Probability
In the following questions 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices :
#35Conditional Probability
A building contractor undertakes a job to construct 4 flats on a plot along with parking area. Due to strike the probability of many construction workers not being present for the job is $0{\cdot}65$ . The probability that many are not present and still the work gets completed on time is $0{\cdot}35$ . The probability that work will be completed on time when all workers are present is $0{\cdot}80$ . Let : $E_1$ : represent the event when many workers were not present for the job; $E_2$ : represent the event when all workers were present; and E : represent completing the construction work on time. Based on the above information, answer the following questions :
#36Conditional Probability
#37Conditional Probability
#38Conditional Probability
Recent studies suggest that roughly 12% of the world population is left handed. Depending upon the parents, the chances of having a left handed child are as follows : A : When both father and mother are left handed : Chances of left handed child is 24%. B : When father is right handed and mother is left handed : Chances of left handed child is 22%. C : When father is left handed and mother is right handed : Chances of left handed child is 17%. D : When both father and mother are right handed : Chances of left handed child is 9%. Assuming that $P(A) = P(B) = P(C) = P(D) = \frac{1}{4}$ and L denotes the event that child is left handed. Based on the above information, answer the following questions :
#39Conditional Probability
Recent studies suggest that roughly 12% of the world population is left handed. Depending upon the parents, the chances of having a left handed child are as follows : A : When both father and mother are left handed : Chances of left handed child is 24%. B : When father is right handed and mother is left handed : Chances of left handed child is 22%. C : When father is left handed and mother is right handed : Chances of left handed child is 17%. D : When both father and mother are right handed : Chances of left handed child is 9%. Assuming that $P(A) = P(B) = P(C) = P(D) = \frac{1}{4}$ and L denotes the event that child is left handed. Based on the above information, answer the following questions :
#40Conditional Probability
#41Conditional Probability
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 : The Venn diagram below represents the probabilities of three different types of Yoga, A, B and C performed by the people of a society. Further, it is given that probability of a member performing type C Yoga is $0{\cdot}44$ . On the basis of the above information, answer the following questions :
#42Conditional Probability
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 : The Venn diagram below represents the probabilities of three different types of Yoga, A, B and C performed by the people of a society. Further, it is given that probability of a member performing type C Yoga is $0{\cdot}44$ . On the basis of the above information, answer the following questions :
#43Conditional Probability
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 : The Venn diagram below represents the probabilities of three different types of Yoga, A, B and C performed by the people of a society. Further, it is given that probability of a member performing type C Yoga is $0{\cdot}44$ . On the basis of the above information, answer the following questions :
#44Conditional Probability
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 : The Venn diagram below represents the probabilities of three different types of Yoga, A, B and C performed by the people of a society. Further, it is given that probability of a member performing type C Yoga is $0{\cdot}44$ . On the basis of the above information, answer the following questions :
#45Conditional Probability
#46Conditional Probability
#47Conditional Probability
#48Conditional Probability
#49Conditional Probability
#50Conditional Probability

Showing the first 50 of 179.

See all 179 questions

Send them this chapter's questions. It's free for them too.

Probability

Studying this with friends?

More chapters in this subject