Skip to main content
Yukti Vault

Statistics & Probability

Probability: JEE Main & Advanced PYQs

372 previous year questions on Probability from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

Practice this chapter

Questions 251-300 of 372

  1. A pair of fair dice is rolled together till a sum of either $5$ or $7$ is obtained. Then the probability that $5$ comes before $7$ is ______.
  2. Let $A,B,C$ be three mutually independent events. Consider the two statements $S_1$ and $S_2$: $S_1$: $A$ and $B\cup C$ are independent $S_2$: $A$ and $B\cap C$ are …
  3. A man takes a step forward with probability $0.4$ and backwards with probability $0.6$. Find the probability that at the end of eleven steps he is one step away from the …
  4. $E$ and $F$ are two independent events. The probability that both $E$ and $F$ happen is $1/12$ and the probability that neither $E$ nor $F$ happens is $1/2$. Then,
  5. India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points $0$, $1$ and $2$ are $0.45$, $0.05$ and $0.50$ …
  6. If $E$ and $F$ are independent events such that $0<P(E)<1$ and $0<P(F)<1$, then
  7. In a certain city only two newspapers $A$ and $B$ are published, it is known that $25\%$ of the city population reads $A$ and $20\%$ reads $B$ while $8\%$ reads both $A$ …
  8. Urn $A$ contains $6$ red and $4$ black balls and urn $B$ contains $4$ red and $6$ black balls. One ball is drawn at random from urn $A$ and placed in urn $B$. Then one …
  9. A lot contains $20$ articles. The probability that the lot contains exactly $2$ defective articles is $0.4$ and the probability that the lot contains exactly $3$ …
  10. A student appears for tests $I$, $II$ and $III$. The student is successful if he passes either in tests $I$ and $II$ or tests $I$ and $III$. The probabilities of student …
  11. There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. …
  12. Two numbers are selected randomly from the set $S=\{1,2,3,4,5,6\}$ without replacement one by one. The probability that minimum of the two numbers is less than $4$ is
  13. 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 …
  14. If $p$ and $q$ are chosen randomly from the set $\{1,2,3,4,5,6,7,8,9,10\}$, with replacement, determine the probability that the roots of the equation $x^{2}+px+q=0$ are …
  15. Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals
  16. If $\overline E$ and $\overline F$ are the complementary events of events $E$ and $F$ respectively and if $0<P(F)<1$, then
  17. For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the $1^{st}$ exam is $p$. If he fails in one of the exams then …
  18. Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals
  19. Eight players $P_1,P_2,\ldots,P_8$ play a knock-out tournament. It is known that whenever the players $P_i$ and $P_j$ play, the player $P_i$ will win if $i<j$. Assuming …
  20. An urn contains $m$ white and $n$ black balls. A ball is drawn at random and is put back into the urn along with $k$ additional balls of the same colour as that of the …
  21. Let $0<P(A)<1$, $0<P(B)<1$ and $P(A\cup B)=P(A)+P(B)-P(A)P(B)$ then
  22. 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 ball is drawn at random, then the …
  23. $A$ is targeting to $B$, $B$ and $C$ are targeting to $A$. Probability of hitting the target by $A$, $B$ and $C$ are $\dfrac23$, $\dfrac12$ and $\dfrac13$ respectively. …
  24. The probability of India winning a test match against West Indies is $1/2$. Assuming independence from match to match the probability that in a $5$ match series India's …
  25. An unbiased die, with faces numbered $1,2,3,4,5,6$, is thrown $n$ times and the list of $n$ numbers showing up is noted. What is the probability that, among the numbers …
  26. A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss equals
  27. Three players, $A,B$ and $C$, toss a coin cyclically in that order (that is $A,B,C,A,B,C,A,B,\ldots$) till a head shows. Let $p$ be the probability that the coin shows a …
  28. If the integers $m$ and $n$ are chosen at random from $1$ to $100$, then the probability that a number of the form $7^{m}+7^{n}$ is divisible by $5$ equals
  29. A box contains $N$ coins, $m$ of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is $1/2$, while it is $2/3$ when a …
  30. The probabilities that a student passes in Mathematics, Physics and Chemistry are $m$, $p$ and $c$ respectively. Of these subjects, the student has a $75\%$ chance of …
  31. 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. Let $u_i$ be the event of selecting $i^{th}$ …
  32. 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. Let $u_i$ be the event of selecting $i^{th}$ …
  33. A box contains $12$ red and $6$ white balls. Balls are drawn from the box one at a time without replacement. If in $6$ draws there are at least $4$ white balls, find the …
  34. A person goes to office either by car, scooter, bus or train, the probability of which being $\dfrac17,\dfrac37,\dfrac27$ and $\dfrac17$ respectively. The probability …
  35. If three distinct numbers are chosen randomly from the first $100$ natural numbers, then the probability that all three of them are divisible by both $2$ and $3$ is
  36. A six faced fair dice is thrown until $1$ comes, then the probability that $1$ comes in an even number of trials is
  37. If $P(B)=\dfrac34$, $P\left(A\cap B\cap\overline C\right)=\dfrac13$ and $P\left(\overline A\cap B\cap\overline C\right)=\dfrac13$, then $P(B\cap C)$ is
  38. 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. Let $u_i$ be the event of selecting $i^{th}$ …
  39. Bag $A$ contains $9$ white and $8$ black balls, while bag $B$ contains $6$ white and $4$ black balls. One ball is randomly picked up from the bag $B$ and mixed up with …
  40. Two distinct numbers $a$ and $b$ are selected at random from $1,2,3,\ldots,50$. The probability that their product $ab$ is divisible by $3$ is :
  41. From the first $100$ natural numbers, two numbers first $a$ and then $b$ are selected randomly without replacement. If the probability that $a-b\ge10$ is $\frac mn$ …
  42. The probability distribution of a random variable $X$ is given below …
  43. 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 set $P(S)\times P(S)$ such that …
  44. A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the …
  45. A bag contains $(N+1)$ coins $-$ $N$ fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is …
  46. A number is chosen at random from the set $\{1,2,3,\ldots,2000\}$. Let $p$ be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the …
  47. If a random variable $x$ has the probability distribution $\begin{array}{c|cccccccc}x&0&1&2&3&4&5&6&7\\\hline P(x)&0&2k&k&3k&2k^2&2k&k^2+k&7k^2\end{array}$ then …
  48. A random variable $X$ takes values $0,1,2,3$ with probabilities $\frac{2a+1}{30},\frac{8a-1}{30},\frac{4a+1}{30},b$ respectively, where $a,b\in\mathbf{R}$. Let $\mu$ and …
  49. From a lot containing $10$ defective and $90$ non-defective bulbs, $8$ bulbs are selected one by one with replacement. Then the probability of getting at least $7$ …
  50. A bag contains $10$ balls out of which $k$ are red and $(10-k)$ are black, where $0\le k\le10$. If three balls are drawn at random without replacement and all of them …

Other chapters