Statistics and Probability — practice questions

108 curated practice questions from Statistics and Probability (Mathematics JEE Advanced, NTA Exams) — 53 hard, 55 medium. Every question includes the final answer free; step-by-step worked solutions with a free account.

• Mr. Dupont is a professional wine taster. When given a French wine, he will identify it with probability 0.9 correctly…
• If E and F are independent events such that and then
• Let A and B are two events such that P(A) > 0 . Assertion : If P (A) + P (B) > 1, then P (B/A) ≥ 1 – P (B’)/P(A) Reason…
• Fifteen coupons are numbered 1, 2, 3,..., 15 respectively. Seven coupons are selected at random one at a time with…
• Let C 1 and C 2 be two biased coins such that the probabilities of getting head in a single toss are 2/3 and 1/3…
• Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the…
• Suppose that Box-I contains 8 red, 3 blue and 5 green balls, Box-II contains 24 red, 9 blue and 15 green balls, Box-III…
• A box contains 5 red and 4 white marbles. Two marbles are drawn successively from the box without replacement and the…
• The probability that an event A happens in one trial of an experiment is 0.4. Three independent trials of these…
• A box contains a normal coin and a double headed coin. A coin selected at random and tossed twice, fell headwise on…
• Three identical dice are rolled. The probability that the same number will appear on each of them, is
• If M and N are two events, the probability that exactly one of them occurs is
• A and B play a game of tennis. The situation of the game is as follows; if one scores two consecutive points after a…
• It is given that the event A and B are such that P ( ~A )= 1 4 , P ( ~A ~B )= 1 2 and P ( ~B ~A )= 2 3 . Then P (B) is
• Let E C denote the complement of an event E . Let E, F, G be pairwise independent events with P ( G ) > 0 and P ( E ∩ F…
• The probabilities of events, A ∩ B, A, B & A ∪ B are respectively in A.P. with probability of second term equal to the…
• If E and F are events with P ( E ) ≤ P ( F ) and P ( E ∩ F ) > 0, then
• Read the passage given below carefully before attempting these questions. A standard deck of playing cards has 52…
• A and B are two events such that P(A) = 0.2 and P(A B) = 0.7 . If A and B are independent events then P(B) equals
• Let X and Y be two events such that P(X / Y)= 1 2 and P(Y / X)= 2 5 . Then
• Lot A consists of 3G and 2D articles. Lot B consists of 4G and 1D article. A new lot C is formed by taking 3 articles…
• Assume that the birth of a boy or girl to a couple to be equally likely, mutually exclusive, exhaustive and independent…
• The probability that atleast one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability…
• Read the passage given below carefully before attempting these questions. A standard deck of playing cards has 52…
• Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r 1 , r 2 and r 3 are the…
• From an urn containing six balls, 3 white and 3 black ones, a person selects at random an even number of balls (all the…
• Let S and T are two events defined on a sample space with probabilities P(S) = 0.5, P(T) = 0.69, P(S/T) = 0.5 Events S…
• A bowl has 6 red marbles and 3 green marbles. The probability that a blind folded person will draw a red marble on the…
• A computer producing factory has only two plants T 1 and T 2 . Plant T 1 produces 20% and plant T 2 produces 80% of the…
• Let E and F be two independent events. The probability that exactly one of them occurs is and the probability of none…
• India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0…
• A JEE aspirant estimates that she will be successful with an 80 percent chance if she studies 10 hours per day, with a…
• A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing…
• For the three events A , B , C, P (exactly one of A or B occurs) = P (Exactly one of B or C occurs) = P (Exactly one of…
• On a Saturday night 20% of all drivers in U.S.A. are under the influence of alcohol. The probability that a driver…
• If and are the complementary events of events E and F respectively and if 0 P ( E ) < 1, then
• Three students S 1 , S 2 , and S 3 are given a problem to solve. Consider the following events: U : At least one of S 1…
• If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three…
• Let S and T are two events defined on a sample space with probabilities P(S) = 0.5, P(T) = 0.69, P(S/T) = 0.5 The value…
• Two cards are drawn from a well shuffled pack of 52 playing cards one by one. If A : the event that the second card…
• If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one…
• A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required. The conditional…
• A bag contains 3 R & 3 G balls and a person draws out 3 at random. He then drops 3 blue balls into the bag & again…
• Read the passage given below carefully before attempting these questions. A standard deck of playing cards has 52…
• A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student…
• An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the…
• Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one…
• Football teams T 1 and T 2 have to play two games against each other. It is assumed that the outcomes of the two games…
• There are three bags B 1 , B 2 and B 3 . The bag B 1 contains 5 red and 5 green balls, B 2 contains 3 red and 5 green…
• Events A and C are independent. If the probabilities relating A, B and C are P (A) = 1/5; P (B) = 1/6 ; P (A ∩ C) =…
• A fair die is rolled. The probability that the first time 1 occurs at the even number of trials is
• If A and B are two independent events such that P (A) > 0, and P (B) ≠ 1, then is equal to
• Let 0 P(A ∪ B) = P(A) + P(B) − P(A). P( b), then :
• Let U 1 and U 2 be two urns such that U 1 contains 3 white and 2 red balls, and U 2 contains only 1 white ball. A fair…
• If (1+3 p ) 3 , (1- p ) 4 (1-2 p ) 2 are the probabilities of three mutually exclusive events defined on a sample space…
• The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to match the…
• A fair die is tossed eight times. Probability that on the eighth throw a third six is observed is,
• A box contains 24 identical balls of which 12 are white and 12 are black. The balls are drawn at random from the box…
• Let A and E by any two events with positive probabilities: Statement 1 : P(E/A) ≥ P(A/E) P(E) Statement 2 : P(A/E) ≥…
• If E 1 and E 2 are two events such that P(E 1 ) = 1/4, P(E 2 /E 1 ) =1/2 and P(E 1 / E 2 ) = 1/4
• A purse contains 2 six sided dice. One is a normal fair die, while the other has 2 ones, 2 threes, and 2 fives. A die…
• Indicate the correct order sequence in respect of the following : I. If the probability that a computer will fail…
• Four persons independently solve a certain problem correctly with probabilities 1 2 , 3 4 , 1 4 , 1 8 . Then the…
• One purse contains 6 copper coins and 1 silver coin ; a second purse contains 4 copper coins. Five coins are drawn from…
• Consider the system of equations ax + by = 0, cx + dy = 0, where a , b , c , d ∈ 0, 1 . Statement-1 : The probability…
• If E and F are the complementary events of E and F respectively and if 0 < P (F) < 1, then
• Consider three sets E 1 = 1, 2, 3 , F 1 = 1, 3, 4 and G 1 = 2, 3, 4, 5 . Two elements are chosen at random, without…
• If A & B are two events such that P(B) ≠ 1, B C denotes the event complementry to B, then
• Let E , F and G be three events having probabilities ext and let P(E F G)= 1 10 . For any event H , if H c denotes its…
• Two real numbers, x & y are selected at random. Given that 0 ≤ x ≤ 1 ; 0 ≤ y ≤ 1 . Let A be the event that y 2 ≤ x ; B…
• An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4…
• A number x is chosen at random from the set 1, 2, 3, 4..... 100 . Define the event: A = the chosen number x satisfies…
• There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random…
• An instrument consists of two units. Each unit must function for the instrument to operate. The reliability of the…
• Two events A and B have probabilities 0.25 and 0.50 respectively the probability that both A and B occur simultaneously…
• For any two events A and B in a sample space
• A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or test I…
• A JEE aspirant estimates that she will be successful with an 80 percent chance if she studies 10 hours per day, with a…
• Let X and Y be two events such that P(X Y)= 1 2 P(Y X)= 1 3 and P(X Y)= 1 6 Which of the following is(are) correct?
• From an urn containing a white and b black balls, k ( th ball is drawn. Assertion : Probability that (k + 1) th ball…
• Let 0 P ( A ) P ( B ) P ( A ∪ B ) = P ( A ) + P ( B ) – P ( A ) P ( B ) then
• If M & N are independent events such that 0 < P(M) < 1 & 0 < P(N) < 1, then :
• A box has four dice in it. Three of them are fair dice but the fourth one has the number five on all of its faces. A…
• Let A , B , C be three mutually independent events. Consider the two statements S 1 and S 2 S 1 : A and B ∪ C are…
• A fair die is tossed repeatedly. A wins if two consecutive outcomes ∈ 1, 2 & B wins if two consecutive outcomes ∈…
• Box A contains 3 red and 2 blue marbles while box B contains 2 red and 8 blue marbles. A fair coin is tossed. If the…
• The probabilities that a student passes in Mathematics, Physics and Chemistry are m , p and c respectively of these…
• If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form 7 m + 7…
• If A and B are two independent events such that P ( A ) > 0 and P ( B ) ≠ 1 then P( A / B ) is equal to
• There are n different gift coupons, each of which can occupy N(N > n) different envelopes, with the same probability…
• A box B 1 contains 1 white ball, 3 red balls and 2 black balls. Another box B 2 contains 2 white balls, 3 red balls and…
• E and F are two independent events. The probability that both E and F happen is 1/12 and the probability that neither E…
• There are n urns each containing n + 1 balls such that the i th urn contains i white balls and ( n + 1 – i ) red balls…
• A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is
• A bag initially contains one red & two blue balls. An experiment consisting of selecting a ball at random, noting its…
• Let X= (x, y) Z Z : x^ 2 8 + y^ 2 20 Three distinct points P , Q and R are randomly chosen from X . Then the…
• A JEE aspirant estimates that she will be successful with an 80 percent chance if she studies 10 hours per day, with a…
• Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and…
• A number is chosen at random from the numbers 10 to 99 . By seeing the number a man will laugh if product of the digits…
• A child throws 2 fair dice. If the numbers showing are unequal, he adds them together to get his final score. On the…
• Two numbers are selected randomly from the set S = 1, 2, 3, 4, 5, 6 without replacement one by one. The probability…
• A examination consists of 8 questions in each of which one of the 5 alternatives is the correct one. On the assumption…
• Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3, 4, 5 ; and box 3…
• Let H 1 , H 2 , ..., H n be mutually exclusive and exhaustive events with P ( H i ) > 0, i = 1, 2, ..., n . Let E be…
• Let S and T are two events defined on a sample space with probabilities P(S) = 0.5, P(T) = 0.69, P(S/T) = 0.5 The value…
• A ship is fitted with three engines E 1 , E 2 and E 3 . The engines function independently of each other with…
• Four fair dice D 1 , D 2 , D 3 and D 4 each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled simultaneously…
• Read the passage given below carefully before attempting these questions. A standard deck of playing cards has 52…

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