Classical and Axiomatic Probability

JEE Main Mathematics · Probability · 30 questions, latest first

• From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P.…20264 April, Shift 2 · Q21
• A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the…20262 April, Shift 2 · Q8
• Let a, b, c ∈{1,2,3,4}. If the probability, that a x^2+2 √2 b x+c>0 for all x ∈ R, is m/n, gcd(m, n)=1, then m+n is equal to ____.20262 April, Shift 1 · Q23
• Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of choosing an ordered pair (A, B) from the…202624 January, Shift 2 · Q22
• From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability…202623 January, Shift 1 · Q23
• Two distinct numbers a and b are selected at random from 1,2,3, …, 50. The probability, that their product a b is divisible by 3,…202622 January, Shift 1 · Q7
• Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, x>y, be 8 and 16 respectively. Two numbers are chosen from…202621 January, Shift 1 · Q8
• The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers…20254 April, Shift 1 · Q8
• Three distinct numbers are selected randomly from the set {1,2,3, …, 40}. If the probability, that the selected numbers are in an…20252 April, Shift 1 · Q25
• Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is…202528 January, Shift 2 · Q8
• Two number k_1 and k_2 are randomly chosen from the set of natural numbers. Then, the probability that the value of…202528 January, Shift 1 · Q9
• Let A=[a_ij] be a square matrix of order 2 with entries either 0 or 1. Let E be the event that A is an invertible matrix. Then…202524 January, Shift 2 · Q8
• A board has 16 squares as shown in the figure: Out of these 16 squares, two squares are chosen at random. The probability that…202523 January, Shift 2 · Q7
• One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1,…202523 January, Shift 1 · Q8
• If an unbiased dice is rolled thrice, then the probability of getting a greater number in the i^th roll than the number obtained…20249 April, Shift 2 · Q20
• Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1,2,3,4. If…20249 April, Shift 1 · Q30
• Let the sum of two positive integers be 24. If the probability, that their product is not less than 3/4 times their greatest…20248 April, Shift 1 · Q19
• If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to…20246 April, Shift 2 · Q20
• The coefficients a, b, c in the quadratic equation a x^2+b x+c=0 are from the set \{1, 2, 3, 4, 5, 6\}. If the probability of…20245 April, Shift 2 · Q7
• The coefficients a, b, c in the quadratic equation a x^2+b x+c=0 are chosen from the set \{1, 2, 3, 4, 5, 6, 7, 8\}. The…20245 April, Shift 1 · Q19
• Two integers x and y are chosen with replacement from the set \{0, 1, 2, 3,..., 10\}. Then the probability that |x-y|>5, is:202430 January, Shift 1 · Q5
• Let S={M=[a_i j], a_i j ∈{0,1,2}, 1 ≤ i, j ≤ 2} be a sample space and A={M ∈ S: M is invertible } be an event. Then P(A) is equal…202311 April, Shift 1 · Q17
• Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2^N<N! is m/n, where m and n are…202310 April, Shift 1 · Q18
• Three dice are rolled. If the probability of getting different numbers on the three dice is p/q, where p and q are co-prime, then…20236 April, Shift 2 · Q19
• A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the…202330 January, Shift 2 · Q90
• Let S={w_1, w_2, … …} be the sample space associated to a random experiment. Let P(w_n)=(P(w_n-1))/2, n ≥ 2. Let A={2 k+3 l: k, l…202329 January, Shift 2 · Q77
• Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up…202329 January, Shift 1 · Q76
• Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N-2, √(3 N), N+2 are in…202325 January, Shift 2 · Q79
• Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space S={x ∈ Z: x(66-x) ≥…202325 January, Shift 1 · Q78
• Let Ω be the sample space and A ⊆ Ω be an event. Given below are two statements: (S 1): If P(A)=0, then A=∅ (S2): If P(A)=1, then…202324 January, Shift 1 · Q79