New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Probability

56 questions · Mathematics · JEE Advanced

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Advanced
Mathematics
Probability

Probability

56 questions · Mathematics · JEE Advanced

Three students $S_{1}, S_{2},$ and $S_{3}$ are given a problem to solve. Consider the following events: U: At least one of $S_{1}, S_{2},$ and $S_{3}$ can solve the problem, V: $S_{1}$ can solve the problem, given that neither $S_{2}$ nor $S_{3}$ can solve…2025 · Shift 1 · Q18 · MCQ
A factory has a total of three manufacturing units, $M_{1}, M_{2}$ , and $M_{3}$ , which produce bulbs independent of each other. The units $M_{1}, M_{2}$ , and $M_{3}$ produce bulbs in the proportions of $2 : 2 : 1$ , respectively. It is known that $20%$ …2025 · Shift 2 · Q27 · Numerical
A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the…2024 · Shift 1 · Q19 · MCQ
Let $X$ be a random variable, and let $P (X = x)$ denote the probability that $X$ takes the value $x$ . Suppose that the points $(x, P (X = x)), x = 0, 1, 2, 3, 4$ , lie on a fixed straight line in the $x y$ -plane, and $P (X = x) = 0$ for all $x \in R - {0, 1, 2, 3, 4}$ …2024 · Shift 1 · Q30 · Numerical
A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i = 1, 2, 3$ …2024 · Shift 2 · Q26 · Numerical
Let $X = {(x, y) \in Z \times Z : \frac{x ^{2}}{8} + \frac{y ^{2}}{20} < 1$ and $y^{2} < 5 x}$ . Three distinct points $R$ and $R$ are randomly chosen from $X$ . Then the probability that $R$ and $R$ …2023 · Shift 1 · Q23 · MCQ
Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$ , then the probability that the experiment stops with head is :2023 · Shift 2 · Q19 · MCQ
Let $X$ be the set of all five digit numbers formed using 1,2,2,2,4,4,0. For example, 22240 is in $X$ while 02244 and 44422 are not in $X$ . Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional…2023 · Shift 2 · Q27 · Numerical
Consider the $6 \times 6$ square in the figure. Let $A_{1}, A_{2}, \dots, A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_{i}$ and $A_{j}$ are friends if they are adjacent along a row or along a column.… Includes diagram2023 · Shift 2 · Q33 · Numerical
Consider the $6 \times 6$ square in the figure. Let $A_{1}, A_{2}, \dots, A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_{i}$ and $A_{j}$ are friends if they are adjacent along a row or along a column.… Includes diagram2023 · Shift 2 · Q34 · Numerical
In a study about a pandemic, data of 900 persons was collected. It was found that 190 persons had symptom of fever, 220 persons had symptom of cough, 220 persons had symptom of breathing problem, 330 persons had symptom of fever or cough…2022 · Shift 1 · Q21 · Numerical
Two players, $P_{1}$ and $P_{2}$ , play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let $x$ and $y$ denote the readings on the die… Includes table2022 · Shift 1 · Q34 · MCQ
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 contains 1 blue, 12 green and 3 yellow balls, Box-IV contains 10 green, 16 orange and 6 white balls. A ball is chosen…2022 · Shift 2 · Q35 · MCQ
Consider three sets E1 = {1, 2, 3}, F1 = {1, 3, 4} and G1 = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1, and let S1 denote the set of these chosen elements. Let E2 = E1 $-$ S1 and F2 = F1 $\cup$ …2021 · Shift 1 · Q22 · MCQ
Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of…2021 · Shift 1 · Q24 · Numerical
Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of…2021 · Shift 1 · Q25 · Numerical
Let E, F and G be three events having probabilities $P (E) = \frac{1}{8}$ , $P (F) = \frac{1}{6}$ and $P (G) = \frac{1}{4}$ , and let P (E $\cap$ F $\cap$ G) = $\frac{1}{10}$ . For any event H, if Hc denotes the complement, then which of the…2021 · Shift 1 · Q32 · Multiple correct
A number of chosen at random from the set {1, 2, 3, ....., 2000}. Let p be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the value of 500p is .2021 · Shift 2 · Q36 · Numerical
Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are $\frac{2}{3}$ and $\frac{1}{3}$ , respectively. Suppose $α$ is the number of heads that appear when C1 is tossed twice,…2020 · Shift 1 · Q23 · MCQ
The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of…2020 · Shift 2 · Q20 · Numerical
Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6, are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is either a prime number or a perfect square. Suppose the sum turns…2020 · Shift 2 · Q33 · Numerical
There are three bags B1, B2 and B3. The bag B1 contains 5 red and 5 green balls, B2 contains 3 red and 5 green balls, and B3 contains 5 red and 3 green balls. Bags B1, B2 and B3 have probabilities $\frac{3}{10}$ , $\frac{3}{10}$ and $\frac{4}{10}$ …2019 · Shift 1 · Q28 · Multiple correct
Let S be the sample space of all 3 $\times$ 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given by E1 = {A $\in$ S : det A = 0} and E2 = {A $\in$ S : sum of entries of A is 7}. If a matrix is chosen at random…2019 · Shift 1 · Q31 · Numerical
There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i = 1, 2, 3, 4, 5. But, on the examination…2018 · Shift 1 · Q35 · MCQ
There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i = 1, 2, 3, 4, 5. But, on the examination…2018 · Shift 1 · Q36 · MCQ
Let X and Y be two events such that $P (X) = \frac{1}{3}$ , $P (X ∣ Y) = \frac{1}{2}$ and $P (Y ∣ X) = \frac{2}{5}$ . Then2017 · Shift 1 · Q19 · Multiple correct
Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is2017 · Shift 2 · Q22 · MCQ
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 total computers produced. $7$ % of computers produced in the factory turn out to be defective. It is…2016 · Shift 1 · Q21 · MCQ
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 are independent. The probabilities of $T_{1}$ winning, drawing and losing a game against $T_{2}$ are $\frac{1}{2}, \frac{1}{6}$ …2016 · Shift 2 · Q23 · MCQ
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 are independent. The probabilities of $T_{1}$ winning, drawing and losing a game against $T_{2}$ are $\frac{1}{2}, \frac{1}{6}$ …2016 · Shift 2 · Q24 · MCQ
The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least $0.96,$ is2015 · Shift 1 · Q32 · Numerical
Let $n_{1}$ and $n_{2}$ be the number of red and black balls, respectively, in box $I$ . Let $n_{3}$ and $n_{4}$ be the number of red and black balls, respectively, in box $I I .$ One of the two boxes, box $I$ and box $I I,$ …2015 · Shift 2 · Q24 · Multiple correct
Let $n_{1}$ and $n_{2}$ be the number of red and black balls, respectively, in box $I$ . Let $n_{3}$ and $n_{4}$ be the number of red and black balls, respectively, in box $I I .$ A ball is drawn at random from box $I$ …2015 · Shift 2 · Q25 · Multiple correct
Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is2014 · Shift 2 · Q21 · MCQ
Box $1$ contains three cards bearing numbers $1, 2, 3;$ box $2$ contains five cards bearing numbers $1, 2, 3, 4, 5;$ and box $3$ contains seven cards bearing numbers $1, 2, 3, 4, 5, 6, 7.$ A card is drawn from each of the boxes. Let $x_{i}$ be number…2014 · Shift 2 · Q24 · MCQ
Box $1$ contains three cards bearing numbers $1, 2, 3;$ box $2$ contains five cards bearing numbers $1, 2, 3, 4, 5;$ and box $3$ contains seven cards bearing numbers $1, 2, 3, 4, 5, 6, 7.$ A card is drawn from each of the boxes. Let $x_{i}$ be number…2014 · Shift 2 · Q25 · MCQ
Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8} .$ Then the probability that the problem is solved correctly by at least one of them is2013 · Shift 1 · Q37 · MCQ
Of the three independent events $E_{1}, E_{2}$ and $E_{3},$ the probability that only $E_{1}$ occurs is $α,$ only $E_{2}$ occurs is $β$ and only $E_{3}$ occurs is $γ .$ Let the probability $p$ that none of events…2013 · Shift 1 · Q38 · Numerical
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 $4$ black balls. A third box $B_{3}$ contains $3$ white balls, $4$ red balls and $5$ black balls. If $1$ …2013 · Shift 2 · Q25 · MCQ
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 $4$ black balls. A third box $B_{3}$ contains $3$ white balls, $4$ red balls and $5$ black balls. If $2$ …2013 · Shift 2 · Q26 · MCQ
A ship is fitted with three engines $E_{1}, E_{2}$ and $E_{3}$ . The engines function independently of each other with respective probabilities $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{4}$ . For the ship to be operational at least two of its…2012 · Shift 1 · Q24 · Multiple correct
Let $X$ and $Y$ be two events such that $P (X ∣ Y) = \frac{1}{2}, P (Y ∣ X) = \frac{1}{3}$ and $P (X \cap Y) = \frac{1}{6} .$ Which of the following is (are) correct ?2012 · Shift 2 · Q25 · Multiple correct
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. The probability that $D_{4}$ shows a number appearing on one of $D_{1}, D_{2}$ and $D_{3}$ is2012 · Shift 2 · Q26 · MCQ
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 coin is tossed. If head appears then $1$ ball is drawn at random from $U_{1}$ and put into…2011 · Shift 1 · Q36 · MCQ
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 coin is tossed. If head appears then $1$ ball is drawn at random from $U_{1}$ and put into…2011 · Shift 1 · Q37 · MCQ
Let $E$ and $F$ be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability of none of them occurring is $\frac{2}{25}$ . If $P (T)$ denotes the probability of occurrence of…2011 · Shift 2 · Q29 · Multiple correct
Let $ω$ be a complex cube root of unity with $ω e 1.$ A fair die is thrown three times. If $r_{1}, r_{2}$ and $r_{3}$ are the numbers obtained on the die, then the probability that $ω^{r_{1}} + ω^{r_{2}} + ω^{r_{3}} = 0$ …2010 · Shift 1 · Q45 · MCQ
A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received by station A and then transmitted to station $B$ . The probability of each station receving the signal correctly is $\frac{3}{4}$ .…2010 · Shift 2 · Q37 · MCQ
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.The conditional probability that $X \geq 6$ given $X > 3$ equals :2009 · Shift 1 · Q25 · MCQ
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.The probability that $X \geq 3$ equals :2009 · Shift 1 · Q26 · MCQ
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.The probability that X = 3 equals2009 · Shift 1 · Q27 · MCQ
Consider the system of equations $a x + b y = 0; c x + d y = 0,$ where $a, b, c, d$ $\in {0, 1}$ STATEMENT - 1 : The probability that the system of equations has a unique solution is $\frac{3}{8} .$ and STATEMENT - 2 : The probability…2008 · Shift 1 · Q28 · MCQ
An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is :2008 · Shift 2 · Q42 · MCQ
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his…2007 · Shift 1 · Q25 · MCQ
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 any other event with 0 Statement 1 : P(H $_{i}$ | E) > P(E | H $_{i}$ ). P(H $_{i}$ ) for $i = 1, 2, ..., n$ . Statement 2 :…2007 · Shift 1 · Q32 · MCQ
Let $E^{c}$ denote the complement of an event $E .$ Let $E, F, G$ be pairwise independent events with $P (G) > 0$ and $P (E \cap F \cap G) = 0.$ Then $P (E^{c} \cap F^{c} ∣ G)$ equals2007 · Shift 2 · Q8 · MCQ