Probability

CBSE Class 12 Mathematics · 112 board questions from this chapter; 111 listed below, 2022–2026

• The probability that a particular item is available in three shops A, B and C is 4/5, 3/4 and 2/3 respectively. If a person…2026
• The probability that it will rain tomorrow in cities A, B and C is 60 %, 70 % and 80 % respectively. The probability that it will…2026
• A box contains 4 red, 5 blue and 1 green marble. A child randomly takes out a marble from the box, notes down the colour and puts…2026
• If E and F are two independent events such that P(E)=3/10, P(E ∪ F)=1/2, then P(E ∣ F)-P(F ∣ E) is equal to:2026
• If 3 P(A)=P(B)=3/5 and P(A ∣ B)=2/3, then P(A ∪ B) is:2026
• For two events A and B such that P(A) ≠ 0 and P(B) ≠ 1, P(A^′ / B^′)=2026
• Assertion: In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on…2026
• The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy…2026
• 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…2026
• A die is rolled. Consider events: A={1,2,5}, B={3,5}, C={2,3,4,5} and hence find: (i) P(A ∣ C) and P(C ∣ A) (ii) P(A ∩ B ∣ C) and…2026
• In a school, the probability of holding a debate competition is 1/3 and that of a quiz competition is 2/3. In the two…2026
• A survey was conducted on the patients who have undergone knee replacement surgeries. It was found that, Robotic Knee replacement…2026
• Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while…2026
• 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 ₹…2026
• A survey was conducted to find out the success rate of students who qualified the entrance examination by dropping a year after…2026
• 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…2026
• An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be…2026
• If P(A ∪ B)=0 · 9 and P(A ∩ B)=0 · 4, then P(Ā)+P(B̄) is:2025
• Let M and N be two events such that P(M)=0.6, P(N)=0.2 and P(M ∩ N)=0.5, then P(M^′ / N^′) is2025
• If P(A ∪ B)=0.9 and P(A ∩ B)=0.4, then P(Ā)+P(B̄) is:2025
• If E and F are two events such that P(E)>0 and P(F) ≠ 1, then P(Ē / F̄) is2025
• If E and F are two independent events such that P(E)=2/3, P(F)=3/7, then P(E / F̄) is equal to:2025
• In the following probability distribution, the value of p is:2025
• The probability distribution of a random variable X is given by: Then E(X) of distribution is2025
• If A and B are two events such that P(B)=1/5, P(A ∣ B)=2/3 and P(A ∪ B)=3/5, then P(A) is:2025
• If P(A)=1/5, P(B)=3/5 and P(A/B)=2/5, then P(A^′ ∩ B^′) is:2025
• If P(A)=1/7, P(B)=5/7 and P(A ∩ B)=4/7, then P(Ā ∣ B) is:2025
• A box has 4 green, 8 blue and 3 red pens. A student picks up a pen at random, checks its colour and replaces it in the box. He…2025
• Chances that three persons A, B, and C go to the market are 30 %, 60 % and 50 % respectively. The probability that at least one…2025
• A coin is tossed and a card is selected at random from a well shuffled pack of 52 playing cards. The probability of getting head…2025
• A meeting will be held only if all three members A, B and C are present. The probability that member A does not turn up is 0 ·…2025
• Assertion ( A ): If A and B are two events such that P(A ∩ B)=0, then A and B are independent events. Reason (R): Two events are…2025
• 10 identical blocks are marked with ' 0 ' on two of them, ' 1 ' on three of them, ' 2 ' on four of them and ' 3 ' on one of them…2025
• Find the probability distribution of the number of boys in families having three children, assuming equal probability for a boy…2025
• Consider the experiment of tossing a coin. If the coin shows head, toss it again; but if it shows a tail, then throw a die. Find…2025
• The probability distribution of a random variable X is given by: (i) Determine the value of p. (ii) Calculate P(X ≥ 1). (iii)…2025
• The probability distribution for the number of students being absent in a class on a Saturday is as follows: Where X is the…2025
• A die with number 1 to 6 is biased such that P(2)=3/10 and probability of other numbers is equal. Find the mean of the number of…2025
• A person is Head of two independent selection committees I and II. If the probability of making a wrong selection in committee I…2025
• Bag I contains 4 white and 5 black balls. Bag II contains 6 white and 7 black balls. A ball drawn randomly by from bag I is…2025
• A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed three times, find the probability…2025
• The probability that a student buys a colouring book is 0 · 7 and that she buys a box of colours is 0 · 2. The probability that…2025
• A gardener wanted to plant vegetables in his garden. Hence he bought 10 seeds of brinjal plant, 12 seeds of cabbage plant and 8…2025
• Some students are having a misconception while comparing decimals. For example, a student may mention that 78 · 56>78 · 9 as…2025
• Three persons viz. Amber, Bonzi and Comet are manufacturing cars which run on petrol and on battery as well. Their production…2025
• Three persons viz. Amber, Bonzi and Comet are manufacturing cars which run on petrol and on battery as well. Their production…2025
• A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances of their…2025
• A bank offers loan to its customers on different types of interest namely, fixed rate, floating rate and variable rate. From the…2025
• Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy,…2025
• Let E be an event of a sample space S of an experiment, then P(S ∣ E)=2024
• Let E and F be two events such that P(E)=0 · 1, P(F)=0 · 3, P(E ∪ F)=0 · 4, then P(F ∣ E) is:2024
• If P(A ∣ B)=P(A^′ ∣ B), then which of the following statements is true?2024
• The probability distribution of a random variable X is: where k is some unknown constant. The probability that the random…2024
• If A and B are events such that P(A / B)=P(B / A) ≠ 0, then:2024
• A pair of dice is thrown simultaneously. If X denotes the absolute difference of the numbers appearing on top of the dice, then…2024
• The chances of P, Q and R getting selected as CEO of a company are in the ratio 4: 1: 2 respectively. The probabilities for the…2024
• Bag I contains 3 red and 4 black balls, Bag II contains 5 red and 2 black balls. Two balls are transferred at random from Bag I…2024
• An urn contains 3 red and 2 white marbles. Two marbles are drawn one by one with replacement from the urn. Find the probability…2024
• A card from a well shuffled deck of 52 playing cards is lost. From the remaining cards of the pack, a card is drawn at random and…2024
• E and F are two independent events such that P(Ē)=0.6 and P(E ∪ F)=0 · 6. Find P(F) and P(Ē ∪ F̄).2024
• The random variable X has the following probability distribution where a and b are some constants: If the mean E(X)=3, then find…2024
• Airplanes are by far the safest mode of transportation when the number of transported passengers are measured against personal…2024
• Self-study helps students to build confidence in learning. It boosts the self-esteem of the learners. Recent surveys suggested…2024
• According to recent research, air turbulence has increased in various regions around the world due to climate change. Turbulence…2024
• Rohit, Jaspreet and Alia appeared for an interview for three vacancies in the same post. The probability of Rohit's selection is…2024
• A departmental store sends bills to charge its customers once a month. Past experience shows that 70 % of its customers pay their…2024
• Ashima can hit a target 2 out of 3 times. She tried to hit the target twice. The probability that she missed the target exactly…2023
• If for two events A and B, P(A-B)=1/5 and P(A)=3/5, then P(B/A) is equal to 12023
• X and Y are independent events such that P(X ∩ Ȳ)=2/5 and P(X)=3/5. Then P(Y) is equal to:2023
• If A and B are two events such that P(A / B)=2 × P(B / A) and P(A)+P(B)=2/3, then P(B) is equal to2023
• 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…2023
• If P(A/B)=0 · 3, P(A)=0 · 4 and P(B)=0 · 8, then P(B/A) is equal to:2023
• If P(A ∩ B)=1/8 and P(Ā)=3/4, then P(B/A) is equal to:2023
• For two events A and B, if P(A)=0 · 4, P(B)=0 · 8 and P(B / A)=0 · 6, then P(A ∪ B) is:2023
• The events E and F are independent. If P(E)=0 · 3 and P(E ∪ F)=0 · 5, then P(E / F)-P(F / E) equals:2023
• If for any two events A and B, P(A)=4/5 and P(A ∩ B)=7/10, then P(B / A) is equal to2023
• Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is2023
• If A and B are two independent events such that P(A)=1/3 and P(B)=1/4, then P(B^′ / A) is2023
• The probability that A speaks the truth is 4/5 and that of B speaking the truth is 3/4. The probability that they contradict each…2023
• Assertion: Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes…2023
• Two fair dice are thrown simultaneously. If X denotes the number of sixes, find the mean of X.2023
• The probability distribution of a random variable X is given below: (i) Find the value of k. (ii) Find P(1 ≤ X<3). (iii) Find…2023
• Two balls are drawn at random one by one with replacement from an urn containing equal number of red balls and green balls. Find…2023
• From a lot of 30 bulbs which include 6 defective bulbs, a sample of 2 bulbs is drawn at random one by one with replacement. Find…2023
• Two numbers are selected from first six even natural numbers at random without replacement. If X denotes the greater of two…2023
• A pair of dice is thrown simultaneously. If X denotes the absolute difference of numbers obtained on the pair of dice, then find…2023
• In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/5 be the probability that…2023
• Recent studies suggest that roughly 12 % of the world population is left handed. Depending upon the parents, the chances of…2023
• There are different types of Yoga which involve the usage of different poses of Yoga Asanas, Meditation and Pranayam as shown in…2023
• A building contractor undertakes a job to construct 4 flats on a plot along with parking area. Due to strike the probability of…2023
• An octagonal prism is a three-dimensional polyhedron bounded by two octagonal bases and eight rectangular side faces. It has 24…2023
• A bag contains 3 red and 4 white balls. Three balls are drawn at random, one-by-one without replacement from the bag. If the…2022
• A coin is tossed twice. The following table shows the probability distribution of number of tails: Find the value of K. Is the…2022
• Three friends A, B and C got their photograph clicked. Find the probability that B is standing at the central position, given…2022
• Let X be a random variable which assumes values x_1, x_2, x_3, x_4 such that 2 P(X=x_1)=3 P(X=x_2)=P(X=x_3)=5 P(X=x_4). Find the…2022
• A pair of dice is thrown. It is given that the sum of numbers appearing on both dice is an even number. Find the probability that…2022
• Let A and B be two events such that P(A)=5/8, P(B)=1/2 and P(A / B)=3/4. Find the value of P(B / A).2022
• Two balls are drawn at random from a bag containing 2 red balls and 3 blue balls, without replacement. Let the variable X denotes…2022
• Probabilities of A and B solving a specific problem are 2/3 and 3/5, respectively. If both of them try independently to solve the…2022
• Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the…2022
• Events A and B are such that P( A)=1/2, P( B)=7/12 and P(Ā ∪ B̄)=1/4 Find whether the events A and B are independent or not. OR…2022
• There are two bags. Bag I contains 1 red and 3 white balls, and Bag II contains 3 red and 5 white balls. A bag is selected at…2022
• A pair of dice is thrown and the sum of the numbers appearing on the dice is observed to be 7. Find the probability that the…2022
• Three persons A, B and C apply for a job of manager in a private company. Chances of their selection are in the ratio 1: 2: 4.…2022
• A man is known to speak truth 7 out of 10 times. He threw a pair of dice and reports that doublet appeared. Find the probability…2022
• A card from a pack of 52 playing cards is lost. From the remaining cards, 2 cards are drawn at random without replacement, and…2022
• In a factory, machine A produces 30% of total output, machine B produces 25% and the machine C produces the remaining output. The…2022
• There are two boxes, namely box-I and box-II. Box-I contains 3 red and 6 black balls. Box-II contains 5 red and 5 black balls.…2022
• A shopkeeper sells three types of flower seeds A1, A2, A3. They are sold in the form of a mixture, where the proportions of these…2022
• 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.…2022
• In a game of Archery, each ring of the Archery target is valued. The centremost ring is worth 10 points and rest of the rings are…2022

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