Statistics and Probability — practice questions

154 curated practice questions from Statistics and Probability (Mathematics JEE Main, NTA Exams) — 118 easy, 21 medium, 15 hard. Every question includes the final answer free; step-by-step worked solutions with a free account.

• Given below are two statements. One is labelled as Assertion and the other is labelled as Reason. STATEMENT - 1…
• Cards are drawn one by one at random from a well shuffled pack of 52 cards until 2 spades are obtained for the first…
• If the mean deviation of numbers 1_ 1 1+d_ 1 1+2 d_ 1 .1+100 d from their mean is 255, then d is equal to
• Let A and B be two independent events such that P(A)= 1 3 and P(B)= 1 6 . Then which of the following is TRUE?
• The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80 . Then which one of the following gives possible…
• For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2…
• Let x 1 , x 2 , x 3 , x 4 and x 5 be the observations with mean m and standard deviation s. Then, standard deviation of…
• The correlation coefficient of two variables x and y is 0.8. The regression coefficient of y on x is 0.2, then the…
• A coin is tossed n times. The probability of getting at least one head is greater than that of getting at least two…
• Given below are two statements. Let x_ 1 , x_ 2 , x_ 3 x_ n be n observations, and let x be their arithmetic mean and ^…
• Three persong P, Q and R independently try to hit a target. If the probabilities of their hitting the target are 3 4 …
• The probability that an event A happens in one trial of an experiment is 0.4. Three independent trials of the…
• The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is
• If each observation of a raw data whose variance is ^ 2 , is increased by , then the variance of the new set is
• If X and Y are the independent random variables B (5, 1 2 ) and B (7, 1 2 ) , then P ( X + Y 1)=
• The mode of a set of observations 7, 12, 8, 5, 6, 4, 9, 10, 8, 9, 7, 9, 6, 5, 9 is
• Statement–I: The average marks of boys in a class is 52 and that of girls is 42 . The average marks of boys and girls…
• A coin is tossed 7 times. Each time a man calls head. The probability that he wins the toss on more occasions is
• 2n boys are randomly divided into two subgroups containing n boys each. The probability that the two tallest boys are…
• The mean age of a combined group of men and women is 25 yrs. If the mean age of the group of men is 26 and that of the…
• A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is
• Three athletes A, B and C participate in a race. Both A and B have the same probability of wining the race and each is…
• Two numbers x and y chosen at random (without replacement) from amongst the numbers 1,2,3, , 3 n . Then the probability…
• Four cards are drawn from a pack of 52 cards. The probability of getting exactly two kings and two clubs is
• The A.M. of n observations is M. If the sum of n–4 observations is a, then the mean of remaining 4 observations is
• 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…
• Consider 5 independent Bernoulli's trials each with probability of success p. If the probability of at least one…
• A letter is known to have come either from LONDON or CLIFTON; on the postmark only the two consecutive letters ON are…
• The probability of guessing correctly at least 8 out of 10 answers on a true-false examination is
• The probability that certain electronic component fails when first used is 0.10. If it does not fail immediately, the…
• A problem in mathematics is given to three student A, B, C and their respective probability of Explanation:ing the…
• If each observation of a raw data whose variance is ^ 2 , is multiplied by , then the variance of the new set is
• In an experiment with 15 observations on x , the following results were available: x^ 2 =2830, x=170 One observation…
• The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
• Let a random variable X have a binomial distribution with mean 8 and variance 4. If P(X 2)= k z^ 15 , then k is equal…
• A & B are two independent witnesses (i.e. no collusion between them). The probability that A will speak the truth is x…
• Nine tokens numbered (1,2, , 9) are equally distributed among three men. The probability that sum of tokens of each…
• One hundred identical coins, each with probability p of showing up heads, are tossed once. If 0<p<1 and the probability…
• The probability that A speaks truth is 4/5, while this probability for B is 3/4. The probability that they contradict…
• Let E and F be two independent events. The probability that both E and F happen is 1 12 and the probability that…
• 6 ordinary dice are rolled. The probability that at least half of them will show at least 3 is
• The probability that an automobile will be stolen and found within one week is 0.0006. The probability that an…
• Three numbers are selected from the set 1,2,3, , 10 . The probability that all the selected numbers are consecutive or…
• Five horses are in race. Mr. A selects two horses at random and bets on them. The probability that Mr. A selected the…
• Consider any set of observations x 1 , x 2 , x 3 ,....,x 101 ; such that x 1 2 3 101 ; then the mean deviation of this…
• If _ i=1 ^ 2 (x_ i -5 )=9 and _ i=1 ^ 2 (x_ i -5 )^ 2 =45 , then the standard deviation of the 9 terms x 1 , x 2 , …
• If the integers m and n belongs to set of first hundred natural numbers then the probability that a number of the form…
• If A and B are independent events such that 0 < P (A) < 1 and 0 < P (B) < 1, then which of the following is not correct…
• Given below are two statements. One is labelled as Assertion and the other is labelled as Reason. STATEMENT - 1…
• Ram and Shyam throw with one dice for a prize of Rs 88 which is to be won by the player who throws 1 first. If Ram…
• A certain player, say X, is know to win with probability 0.3 if the track is fast and 0.4 if the track is slow. For…
• How many times must a man toss a fair coin so that the probability of having atleast one head is more than 90%?
• If the arithmetic mean of the numbers x 1 , x 2 , x 3 ,...........,x n is , then the arithmetic mean of numbers ax 1 +…
• A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The…
• The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher be included, the…
• In an experiment with 15 observations on x, the following results were available. x^ 2 =2830, x=170 One observation…
• A square is inscribed in a circle. If p 1 is the probability that a randomly chosen point of the circle lies within the…
• Let A = 2, 3, 4, ...., 20, 21 . A number is chosen at random from the set A and it is found to be a prime number. The…
• Let a, b, c, d and e be the observations with mean m and standard deviation s. The standard deviation of the…
• If for some x R, the frequency distribution of the marks obtained by 20 students in a test is: Marks 2 3 5 7 Frequency…
• The mean of five observations is 4 and their variance is 5.2 . If three observations are 1, 2, and 6, the other two are
• Fifteen coupons are numbered 1, 2, ..., 15, respectively. Seven coupons are selected at random one at a time with…
• Given below are two statements. A fair die is rolled once. STATEMENT -1: The probability of getting a composite number…
• Given below are two statements. STATEMENT - 1 (Assertion): If A and B are two independent events such that P(A)= 1 2 …
• An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses is…
• A fair coin is tossed repeatedly. If tail appears on first four tosses then the probability of head appearing on fifth…
• A random variable X has the probability distribution X 1 2 3 4 5 6 7 8 P(X) 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05 For…
• 5 girls and 10 boys sit at random in a row having 15 chairs numbered as 1 to 15. Find the probability that end seats…
• A pair of dice is rolled again and again till a total of 5 or a total of 7 is obtained. The chance that a total of 5…
• A and B are events such that is P(A B)= 3 4 , P(A B)= 1 4 , P( A )= 2 3 , then P( A B)
• If probability of a defective bolt is 0.1 , then mean and standard deviation of distribution of bolts in a total of…
• In a certain town, 40% of the people have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes…
• Mean of 5 observations is 7 . If four of these observations are 6, 7, 8, 10 and one is missing, then the variance of…
• A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when…
• For the three events A, B and C, P (exactly one of the events A or B occurs) = P (exactly one of the events B or C…
• A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is
• An unbiased coin is tossed eight times. The probabity of obtaining at least one head and at least one tail is:
• An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers…
• The standard deviation of a variable x is 10. Then the standard deviation of 50 + 5 x is:
• If the mean deviation about the median of the numbers a_ 1 2 a_ 1 . .50 a is 50 , then |a| equals
• The mean of 100 observations is 50 and their standard deviation is 5 . The sum of squares of all observations is
• The median of the variables x+4, x- 7 2 , x- 5 2 , x-3, x-2, x+ 1 2 , x- 1 2 , x+5(x>0) is
• A and B are two events. Odds against A are 2 : 1. Odds in favour of A B are 3 : 1. If x P(B) y , then the ordered pair…
• If v is the variance and is the standard deviation, then
• If the probability of hitting a target by a shooter, in any shot, is 1 3 , then the minimum number of independent shots…
• The number ‘a’ is randomly selected from the set 0, 1, 2, 3, ...... 98, 99 . The number ‘b’ is selected from the same…
• The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent…
• For a biased die the probabilities for the diffferent faces to turn up are given below : Faces : 1 2 3 4 5 6…
• In a betting game in an exhibition two dice P and Q are being used. Dice P has four red faces and two white faces…
• The mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on, it was…
• Let A and B be two events such that P( A B )= 1 6 , P(A B)= 1 4 and P ( ~A )= 1 4 , where A stands for the complement…
• A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one,with replacement, then the…
• The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P (X = 1) is
• The probability that in a year of the 22nd century chosen at random there will be 53 Sundays, is
• India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0…
• The probabilities of four cricketers A, B, C and D scoring more than 50 runs in a match are 1 2 , 1 3 , 1 4 and 1 10 …
• If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains…
• Statement–I: The mean and variance for first n natural numbers are n +1 2 and n ^ 2 +1 12 , respectively. Statement–II…
• If three numbers are selected from the set 1,2,3, 15 without repetition, then the probability that their product is a…
• A man is known to speak truth 3 out of 4 times. He throws a dice and reports that it is six. The probability that it is…
• A pair of numbers is picked up randomly (without replacement) from the set 1, 2, 3, 5, 7, 11, 12, 13, 17, 19 . The…
• A survey of people in a given region showed that 20% were smokers. The probability of death due to lung cancer, given…
• When tested, the lives (in hours) of 5 bulbs were noted as follows : 1357, 1090, 1666, 1494, 1623 The mean deviation…
• One bag contains 5 white and 4 black balls. Another bag contains 7 white and 9 black balls. A ball is transferred from…
• In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the…
• An Urn contains ‘m’ white and ‘n’ black balls. All the balls except for one ball, are drawn from it. The probability…
• Given below are two statements. One is labelled as Assertion and the other is labelled as Reason. STATEMENT - 1…
• An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the…
• The probability that the birthdays of six different people will fall in exactly two calendar months is
• For k = 1, 2,3 the box B k contains k red balls and (k + 1) white balls. Let P ( ~B _ 1 )= 1 2 , P ( ~B _ 2 )= 1 3 and…
• A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without…
• Five coins are tossed simultaneously. The probability of the event that at least one tail turns up, is
• A Urn contains ‘m’ white and ‘n’ black balls. Balls are drawn one by one till all the balls are drawn. Probability that…
• From a pack of cards, 2 cards are drawn at random one by one with replacement. The probability that the first is heart…
• Let x 1 , x 2 ......, x n be n observations. Let _ i = x _ i + k for i = 1, 2,.........,n, where l and k are constants…
• A, B and C are contesting the election for the post of secretary of a club which does not allow ladies to become…
• A, B, C are three events for which P(A) = 0.6, P(B) = 0.4, P(C) = 0.5, P ( ~A ~B )=0.8 , P ( ~A C )=0.3 and P ( ~A ~B C…
• Three groups A, B, C are competing for positions on the Board of Directors of a company. The probabilities of their…
• Suppose that a random variable X follows Binomial distribution with parameters n and p, where 0 < p < 1 . If P (X =…
• Let A and B be two events such that the probability that exactly one of them occurs is 2 5 and the probability that A…
• The mean of a set of observations is x . If each observation is divided by α,α ≠ 0 and then is increased by 10, then…
• Four tickets marked 00, 01, 10 and 11 respectively are placed in bag. A ticket is drawn at random five times, being…
• The variance of 20 observations is 5 . If each observation is multiplied by 2, then the new variance of the resulting…
• A dice is thrown a fixed number of times. If probability of getting even number 3 times is same as the probability of…
• There are four machines and it is known that exactly two of them are faulty. They are tested one by one in a random…
• In a series of 2n observations half of them equal 'a' and remaining equal '-a'. if the standard deviation of the…
• There are n-persons sitting in a row. Two of them are selected at random. The probability that two selected persons are…
• The mean of a B.D. (binomial distribution) is 9 whose S.D. (standard deviation) is 3 / 2 then B.D. is given by
• If P ( ~B )= 3 5 , P ( ~A / B )= 1 2 and P ( ~A ~B )= 4 5 then P ((A ∪ B)’) + P (A’ ∪ B) =
• An unbiased cubic die marked with 1, 2, 2, 3, 3, 3 is rolled 3 times. The probability of getting a total score of 4 or…
• If in a frequency distribution the mean and median are 21 and 22 respectively, then its mode is approximately
• A multiple choice examination has 5 questions. Each question has three alternative answer of which exactly one is…
• If E and F are events with P(E) P(F) and P(E F)>0 , then
• Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at…
• Two coins are available, one fair and the other two headed. Choose a coin and toss it once assume that the unbiased…
• Two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur…
• If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?
• Mean of 100 observations was found to be 45 . It was later found that two observations 19 and 31 were incorrectly…
• The number which indicates variability of data or observations, is called
• In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number…
• In an entrance test there are multiple choice questions. There are four possible answers to each question of which one…
• x 1 , x 2 , x 3 , ...... x 50 are fifty numbers such that x r r + 1 for r = 1, 2, 3, ...., 49 . Five numbers out of…
• Mean deviation about the median for the data 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21 is
• Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without…
• One hundred identical coins, each with probability, p, of showing up heads are tosses once. If 0 < p < 1 and the…
• A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I…
• Three persons A, B and C fire at a target in turn, starting with A. Their probabilities of hitting the target are 0.4…
• Three distinguishable balls are distributed in three cells. The probability that all three occupy the same cell, given…
• The probability of guessing correctly atleast 8 out of 10 answers on a true-false type examination is
• Given below are two statements. STATEMENT - 1: For events A and B of sample space if P ( A E ) P(A) then P ( B A ) P(B)…
• The records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from…
• Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is
• The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased…
• Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three…

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