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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.

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Questions 151-200 of 372

  1. If the probability of hitting a target by a shooter, in any shot is $\frac13$, then the minimum number of independent shots at the target required by him so that the …
  2. For three events $A$, $B$ and $C$ …
  3. It is given that the events $A$ and $B$ are such that $P(A)=\frac14$, $P(A|B)=\frac12$ and $P(B|A)=\frac23$. Then $P(B)$ is :
  4. If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it …
  5. Events $A,B,C$ are mutually exclusive events such that $P(A)=\frac{3x+1}{3}$, $P(B)=\frac{1-x}{4}$ and $P(C)=\frac{1-2x}{2}$. The set of possible values of $x$ are in …
  6. If the mean and the variance of a binomial variate $X$ are $2$ and $1$ respectively, then the probability that $X$ takes a value greater than or equal to one is :
  7. 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 obtained on them is noted. If the toss of the coin …
  8. Two cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. Let $X$ denote the random variable of number of aces obtained in the two drawn …
  9. Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three …
  10. From a group of $10$ men and $5$ women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees …
  11. Two integers are selected at random from the set $\{1,2,\ldots,11\}$. Given that the sum of selected numbers is even, the conditional probability that both the numbers …
  12. A box contains $15$ green and $10$ yellow balls. If $10$ balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :
  13. Let $M$ be the maximum value of the product of two positive integers when their sum is $66$. Let the sample space $S=\left\{x\in Z:x(66-x)\ge\frac59M\right\}$ and the …
  14. There are three rotten apples mixed accidentally with seven good apples and four apples are drawn one by one without replacement. Let the random variable $X$ denote the …
  15. The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least $90\%$ is :
  16. An unbiased coin is tossed $5$ times. Suppose that a variable $X$ is assigned the value $k$ when $k$ consecutive heads are obtained for $k=3,4,5$, otherwise $X$ takes …
  17. If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:
  18. For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is $\frac45$ …
  19. Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter $M$ appears at the fourth position in any …
  20. In a binomial distribution $B(n,p)$, the sum and product of the mean and variance are $5$ and $6$ respectively, then find $6(n+p-q)$ is equal to :-
  21. An urn contains $6$ white and $9$ black balls. Two successive draws of $4$ balls are made without replacement. The probability, that the first draw gives all white balls …
  22. Two newspapers $A$ and $B$ are published in a city. It is known that $25\%$ of the city population reads $A$ and $20\%$ reads $B$ while $8\%$ reads both $A$ and $B$. …
  23. Two squares are chosen at random on a chessboard ($8\times8$ board having $64$ squares). The probability that they have a side in common is :
  24. Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than $99\%$ is :
  25. Let $A$ and $B$ be two non-null events such that $A\subset B$. Then, which of the following statements is always correct?
  26. Let $S=\{w_1,w_2,\ldots\}$ be the sample space associated to a random experiment. Let $P(w_n)=\frac{P(w_{n-1})}{2}$, $n\ge2$. Let $A=\{2k+3l;\ k,l\in\mathbb N\}$ and …
  27. A person throws two fair dice. He wins Rs. $15$ for throwing a doublet (same numbers on the two dice), wins Rs. $12$ when the throw results in the sum of $9$, and loses …
  28. Let a random variable $X$ has a binomial distribution with mean $8$ and variance $4$. If $P(X\le2)=\frac{k}{2^{16}}$, then the value of $k$ is equal to
  29. Assume that each born child is equally likely to be a boy or girl. If two families have two children each, then the conditional probability that all children are girls …
  30. Four persons can hit a target correctly with probabilities $\frac12,\frac13,\frac14$ and $\frac18$ respectively. If all hit at the target independently, then the …
  31. In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $\frac14$. If the probability that at most two machines …
  32. Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N-2$, $\sqrt{3N}$, $N+2$ are in geometric progression be …
  33. In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is …
  34. Two dice are thrown independently. Let $A$ be the event that the number appeared on the $1^{st}$ die is less than the number appeared on the $2^{nd}$ die, $B$ be the …
  35. An integer is chosen at random from the integers $1,2,3,\ldots,50$. The probability that the chosen integer is a multiple of at least one of $4$, $6$ and $7$ is
  36. 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 …
  37. Bag 1 contains $4$ white balls and $5$ black balls, and Bag 2 contains $n$ white balls and $3$ black balls. One ball is drawn randomly from Bag 1 and transferred to Bag …
  38. In a class of $60$ students, $40$ opted for NCC, $30$ opted for NSS and $20$ opted for both NCC and NSS. If one of these students is selected at random, then the …
  39. Let $S$ be the sample space of all $3\times3$ matrices with entries from the set $\{0,1\}$. Let the events $E_1$ and $E_2$ be given by $$E_1=\{A\in S:\det A=0\}\ …
  40. If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces is thrown five times, then the probability that the product of the outcomes is positive, is :
  41. 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 …
  42. 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 balls, and $B_3$ contains 5 red and 3 green …
  43. If $X$ has a binomial distribution, $B(n,p)$ with parameters $n$ and $p$ such that $P(X=2)=P(X=3)$, then $E(X)$, the mean of variable $X$, is :
  44. Let $|X|$ denote the number of elements in a set $X$. Let $S=\{1,2,3,4,5,6\}$ be a sample space, where each element is equally likely to occur. If $A$ and $B$ are …
  45. $A$ and $B$ alternately throw a pair of dice. $A$ wins if he throws a sum of $5$ before $B$ throws a sum of $8$, and $B$ wins if he throws a sum of $8$ before $A$ throws …
  46. A set $S$ contains $7$ elements. A non-empty subset $A$ of $S$ and an element $x$ of $S$ are chosen at random. Then the probability that $x\in A$ is :
  47. 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 on the die. If he decides to throw the die …
  48. Let $A=[a_{ij}]$ be a $2\times2$ matrix such that $a_{ij}\in\{0,1\}$ for all $i$ and $j$. Let the random variable $X$ denote the possible values of the determinant of …
  49. A bag contains $6$ balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least $5$ black balls is
  50. If $A$ and $B$ are two events such that $P(A\cup B)=P(A\cap B)$, then the incorrect statement amongst the following statements is :

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