CBSE Class 11 Mathematics HOTs Probability

Question. If two numbers p and q are choosen randomly from the set {1, 2, 3, 4} with replacement, then the probability that p2 ≥ 4q is equal to
(a) 1/4
(b) 3/16
(c) 1/2
(d) 7/16
Answer : D

Question. A is a set containing n element. A subset P of A is chosen at random, and the set A is reconstruced by replacing the elements of P. Another subset Q of A is now chosen at random. The probability that P È Q contains exactly r elements, 1 ≤ r ≤ n, is
(a) ⁿC_r3r/4ⁿ
(b) 3ⁿ/4ⁿ
(c) ⁿC_r3^n-r/4ⁿ
(d) ⁿC_r3n/4ⁿ
Answer : B

Question. 10 persons sit around a circular table with 10 numbered chairs. The probability that the two particular persons A and B are always together is
(a) 2/9
(b) 1/5
(c) 1/9
(d) 2/5
Answer : A

Question. 5 different games are to be distributed among 4 children randomly. The probability that each child gets atleast one game is
(a) 1/4
(b) 15/64
(c) 21/64
(d) 1/4
Answer : B

Question. A natural number x is chosen at random from the first 100 natural numbers. Then the probability, for the equation x + 100/x > 50 is
(a) 20/1
(b) 20/11
(c) 3/1
(d) 20/3
Answer : B

Question. Two distinct numbers a and b are chosen randomly from the set {2, 2², 2³, .... 2²⁵}. Then the probability that logab is an integer is
(a) 131/300
(b) 31/300
(c) 21/200
(d) 62/300
Answer : B

Question. There are two vans each having numbered seats, 3 in the front and 4 at the back. There are 3 girls and 9 boys to be seated in the vans. The probability of 3 girls sitting together in a back row on adjacent seats, is
(a) 1/13
(b) 1/39
(c) 1/65
(d) 1/91
Answer : D

Question. Ashmit and Bishmit are two students who appeared in Class X exam, Probability that Ashmit will pass is 0.5 while probability that both of them will pass is at least 0.1 and at most 0.3, and probability that Bishmit will pass is P(B) then find the range of P(B)
(a) (0.2, 0.8)
(b) (0.15, 0.25)
(c) (0.1, 0.8)
(d) None of these
Answer : C

Question. A person throws two dice, one the common cube and the other regular tetrahedron with numbers 1, 2, 3, 4 on its faces, the number on the lowest face being taken in the case of a tetrahedron.The chance that the sum of numbers thrown is not
less than 5 is
(a) 4/1
(b) 4/3
(c) 5/4
(d) 6/5
Answer : B

Question. If three squares are chosen at random on a chess board, then find the probability that they should be in a diagonal line
(a) 9/743
(b) 11/743
(c) 13/743
(d) None of these
Answer : D

Question. A box contains 2 fifty paise coins, 5 twenty five paise coins and 15 ten paise coins. Five coins are taken out of the box at random. Probability that the value of these five coins is less than one rupee and fifity paise is
(a) 170/²²C₅
(b) 1 - 150/²²C₅
(c) 1 - 170/²²C₅
(d) None of these
Answer : C

Question. From a well-shuffled pack of 52 cards, four cards are selected at random. The probability of drawing exactly 2 spades and exactly 2 aces is
(a) 1494/270725
(b) 1594/270725
(c) 1296/270725
(d) 1396/270725
Answer : A

Question. For the three events A, B, and C, P (exactly one of the events A or B occurs) = P (exactly one of the two events B or C occurs) = P(exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) = p², where 0 < p < 1/2. Then the probability of at least one of the three events A, B and C occurring is
(a) 3p + 2p²/2
(b) p + 3p²/4
(c) p + 3p²/2
(d) 3p + 2p²/4
Answer : A

Question. If the letters of the word MATHEMATICS are arranged arbitrarily, the probability that C comes before E, E before H, H before I and I before S is
(a) 1/75
(b) 1/24
(c) 1/120
(d) 1/720
Answer : C

Question. In a game of chance a player throws a pair of dice and scores points equal to the difference between the numbers on the two dice. Winner is the person who scores exactly 5 points more than his opponent.
If two players are playing this game only one time, then the probability that neither of them wins is
(a) 1/54
(b) 1/108
(c) 53/54
(d) 107/108
Answer : C

Question. The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chances of the events are
(a) 1/9, 1/3
(b) 1/16, 1/4
(c) 1/4, 1/2
(d) None of these
Answer : A

Question. There are three events E₁, E₂ and E₃. one of which must, and only one can happen. The odds are 7 to 4 against E₁ and 5 to 3 against E₂. The odds against E₃ is
(a) 4 : 11
(b) 3 : 8
(c) 23 : 88
(d) 65 : 23
Answer : D

Numeric Value Answer

Question. Two numbers x and y are chosen at random without replacement from amongst the numbers 1, 2, 3, .........,3n. The probability that x³ + y³ is divisible by 3 is
Answer : 0.33

Question. 5 girls and 10 boys sit at random in a row having 15 chairs numbered as 1 to 15. If the probability that the end seats are occupied by the girls and between any two girls odd number of boys take seat is 20/n then n/1001 is equal to
Answer : 3

Question. A quadratic equation is chosen from the set of all quadratic equations which are unchanged by squaring their roots. If the chance that the chosen equation has equal roots, is p/q, then p + q =
Answer : 3

Question. In a multiple choice question, there are five alternative answers of which one or more than one are correct. A candidate will get marks on the question, if he ticks all the correct answers. If he decides to tick answers at random, then the least number of choice should he be allowed so that the probability of his getting marks on the question exceeds 1/8 is
Answer : 4

Question. A four digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd, is
Answer : 0.50

Question. A die is rolled three times, if p be the probability of getting a large number than the previous number, then the value of 54p is
Answer : 5

Question. The probability that in the random arrangement of the letters of the word ‘UNIVERSITY’, the two I’s does not come together is
Answer : 0.80

Question. A class contains 20 boys and 20 girls of which half the boys and half the girls have cat eyes. If one student is selected from the class & if the probability that either the student is a boy or has cat eyes is a/b, then √a² + b² =
Answer : 5