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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 301-350 of 372

  1. 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 …
  2. If $E$ and $F$ are events with $P(E)\le P(F)$ and $P(E\cap F)>0$, then
  3. 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 $P(E^c\cap F^c\,|\,G)$ equals
  4. Consider the system of equations $ax+by=0$, $cx+dy=0$, where $a,b,c,d\in\{0,1\}$. STATEMENT-1: The probability that the system of equations has a unique solution is …
  5. 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 $B$ …
  6. 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, is
  7. Let $E,F$ and $G$ be three events having probabilities $P(E)=\frac18$, $P(F)=\frac16$ and $P(G)=\frac14$, and let $P(E\cap F\cap G)=\frac{1}{10}$. For any event $H$, if …
  8. 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 replacement, from the set $E_1$, and let $S_1$ …
  9. Let $\omega$ be a complex cube root of unity with $\omega\neq1$. A fair die is thrown three times. If $r_1$, $r_2$ and $r_3$ are the numbers obtained on the die, then …
  10. 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 …
  11. 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 …
  12. 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 …
  13. 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 …
  14. 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?
  15. Of the three independent events $E_1$, $E_2$ and $E_3$, the probability that only $E_1$ occurs is $\alpha$, only $E_2$ occurs is $\beta$ and only $E_3$ occurs is …
  16. 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, is
  17. 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 …
  18. 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, is
  19. Let $C_1$ and $C_2$ be two biased coins such that the probabilities of getting head in a single toss are $\frac23$ and $\frac13$, respectively. Suppose $\alpha$ is the …
  20. 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 …
  21. 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 …
  22. A board has $16$ squares as shown in the figure : [figure: a 4x4 grid of 16 equal squares] Out of these $16$ squares, two squares are chosen at random. The probability …
  23. Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at …
  24. Two numbers $k_1$ and $k_2$ are randomly chosen from the set of natural numbers. Then the probability that the value of $i^{k_1}+i^{k_2}$, ($i=\sqrt{-1}$) is non-zero …
  25. Let $p_i$ be the probability that a randomly chosen point has $i$ many friends, $i=0,1,2,3,4$. Let $X$ be a random variable such that for $i=0,1,2,3,4$, the probability …
  26. Two distinct points are chosen randomly out of the points $A_1, A_2, \ldots, A_{49}$. Let $p$ be the probability that they are friends. Then the value of $7p$ is
  27. For $i=1,2,3,4$, let $T_i$ denote the event that the students $S_i$ and $S_{i+1}$ do NOT sit adjacent to each other on the day of the examination. Then, the probability …
  28. The value of $\frac{625}{4}p_1$ is ___ .
  29. The probability that $x_1+x_2+x_3$ is odd, is
  30. $P(X>Y)$ is
  31. If 1 ball is drawn from each of the boxes $B_1$, $B_2$ and $B_3$, the probability that all 3 drawn balls are of the same colour is
  32. The probability of the drawn ball from $U_2$ being white is
  33. The probability that, on the examination day, the student $S_1$ gets the previously allotted seat $R_1$, and NONE of the remaining students gets the seat previously …
  34. The probability that $X=3$ equals
  35. $P(X=Y)$ is
  36. The value of $\frac{125}{4}p_2$ is ___ .
  37. Given that the drawn ball from $U_2$ is white, the probability that head appeared on the coin is
  38. The probability that $X\ge3$ equals
  39. The probability that $x_1,x_2,x_3$ are in an arithmetic progression, is
  40. If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are …
  41. The conditional probability that $X\ge6$ given $X>3$ equals
  42. An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability …
  43. Cards are drawn one by one at random from a well-shuffled full pack of $52$ playing cards until $2$ aces are obtained for the first time. If $N$ is the number of cards …
  44. A coin has probability $p$ of showing head when tossed. It is tossed $n$ times. Let $p_n$ denote the probability that no two (or more) consecutive heads occur. Prove …
  45. Three numbers are chosen at random without replacement from $\{1,2,3,\ldots,8\}$. The probability that their minimum is $3$, given that their maximum is $6$, is :
  46. $A$ and $B$ are two independent events. $C$ is the event in which exactly one of $A$ or $B$ occurs. Prove that …
  47. A fair coin is tossed $n$ times. If the probability of getting $6$ heads is equal to that of getting $8$ tails, then the probability of getting $2$ heads is
  48. A bag contains four bulbs. Some of these bulbs are defective. Two bulbs are drawn at random and it is found that both the bulbs are defective. What is the probability …
  49. A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :
  50. Three urns $A$, $B$ and $C$ contain $7$ red, $5$ black; $5$ red, $7$ black and $6$ red, $6$ black balls, respectively. One of the urn is selected at random and a ball is …

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