CBSE Class 12 (Science) Probability — practice questions
54 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 12 (Science) Probability in the app →A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?If P(A) = 0.5, P(B) = 0.6, and P(A ∩ B) = 0.2, then P(A ∪ B) is:Two dice are rolled. The probability of getting AT LEAST ONE SIX is:Bayes' theorem is essentially used to:For a discrete random variable X with values 0, 1, 2 and probabilities 0.3, 0.5, 0.2 respectively, the mean E(In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:For a binomial distribution B(n, p), the MEAN and VARIANCE are:The number of ways to choose 3 books out of 5 (order does NOT matter) is:For events E and F with P(F) > 0, P(E|F) is which ratio?Three fair coins are tossed. Given the first shows tail, find P(at least two heads).If P(B) = 9/13 and P(A ∩ B) = 4/13, what is P(A|B)?For an event F with P(F) > 0 in sample space S, P(S|F) equals what?If P(E|F) = 0.35, what is P(E'|F)?If P(F) = 0.4 and P(E|F) = 0.5, find P(E ∩ F).Two cards are drawn one after the other without replacement. P(both aces)?A box has 5 red and 3 blue balls. Two are drawn without replacement. P(both red)?Events E and F, both with nonzero probability, are independent ifE and F are independent, P(E) = 0.3 and P(F) = 0.5. Find P(E ∩ F).A card is drawn from 52. Given it is a spade, P(it is an ace)?A partition of a sample space must have events that areFor a nonempty event E, which pair always forms a partition of S?How many partitions can a given sample space have?E1, E2 partition S: P(E1)=0.6, P(A|E1)=0.2, P(E2)=0.4, P(A|E2)=0.5. Find P(A).Bag I: 3 red, 4 black; Bag II: 5 red, 6 black. Pick a bag at random; P(red)?When Bayes' theorem is applied, the events E1, ..., En are calledIn Bayes' theorem, P(Ei) before observing A is called theBayes' theorem is also called the formula for the probability of what?What problem did John Bayes solve using conditional probability?In which year was Bayes' theorem published posthumously?Whose 1654 correspondence laid the first foundation of probability science?Three dice are thrown. Which total is more likely, 9 or 10?Who discovered the binomial distribution?Which Dutch scientist wrote the first book on probability after Pascal and Fermat?Which Russian mathematician formulated the axiomatic approach to probability?The event E ∩ F is also written in which short form?The event E ∩ F describes which situation?Once F is known to have occurred, E is judged within which sample space?A family has two children. Given at least one is a boy, P(both boys)?Two dice are thrown. Given doubles, P(the sum is 8)?Two dice are thrown. Given the first shows 5, P(sum is at least 10)?One ace is drawn from a deck and kept aside. P(the next card is an ace)?A fair coin is tossed twice. Given the first is tails, P(second is heads)?P(A) = 0.6, P(B) = 0.5, P(A ∩ B) = 0.3. Find P(A|B).A, B independent, P(A) = 0.2, P(B) = 0.5. Find P(A ∩ B').Two archers hit with chances 0.7 and 0.8 independently. P(at least one hits)?A fair coin is tossed 3 times. P(at least one head)?1% are ill; test is + for 90% of ill, 5% of healthy. P(ill | +)?Machine A makes 60% of items (2% faulty), B makes 40% (5% faulty). P(faulty)?Bag I: 2 white, 3 red; Bag II: 4 white, 5 red. A bag is chosen at random. P(white)?Bag I: 2 white, 3 red; Bag II: 4 white, 5 red. A white ball is drawn. P(Bag II)?If P(E ∩ F) = 0.12 and P(F) = 0.4, find P(E|F).In Bayes' theorem, the denominator sum of P(Ej)P(A|Ej) equalsTwo events are independent when one occurringTwo cards are drawn without replacement. P(a king, then a queen)?