Probability: JEE Main Mathematics Previous Year Questions

458 previous year questions from Probability. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. $Four fair dice are thrown independently 27 times. Then the expected number of times, at least twodice show up a three or a five, is$
2. $Let E^{C} denote the complement of an event E . Let E_{1}, E_{2} and E_{3} be any pairwise independent events with P (E_{1}) > 0 and\dots$
3. $Probability of guessing correctly atleast 7 out of 10 answers in a "True" or "False" test is$
4. $Given three indentical bags each containing 10 Balls, whose colours are as follows: Red Blue Green Bag I 3 2 5 Bag II 4 3 3 Bag III 5 1 4 A person chooses a bag at random\dots$
5. $A target is to be destroyed in a bombing exercise and there is a 75 % chance that a bomb will hit the target. Assuming that two direct hits are required to dest\dots$
6. $If the mean and variance of a binomial distribution are 4 and \frac{4}{3} respectively, then P (X = 2) =$
7. $A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls\dots$
8. $A and B each select one number at random from the distinct numbers 1, 2, 3, \dots, n and the probability that the number selected by\dots$
9. $The probability of selecting integers a \in [-5, 30] such that x^{2} + 2(a + 4)x - 5a + 64 > 0, for all x \in R, is:$
10. $One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1, two faces marked 2, two faces marked 3\dots$
11. $When a missile is fired from a ship, the probability that it is intercepted is \frac{1}{3} and the probability that the missile hits the target, given that it is not i\dots$
12. $If A, B, C are three mutually exclusive and exhaustive events of an experiment such that P (A) = 2 P (B) = 3 P (C), the\dots$
13. $Given that A and B are two events such that P (B) = \frac{3}{5}, P (\frac{A}{B}) = \frac{1}{2} and\dots$
14. $Let A and B be two independent events such that P (A) = \frac{1}{3} and P (B) = \frac{1}{6} Then, which of the following is TRUE?$
15. $Four persons can hit a target correctly with probabilities \frac{1}{2}, \frac{1}{3}, \frac{1}{4} and \frac{1}{8} respectively. If all hit at the targeti\dots$
16. $A person P speaks truth in 75 % cases and another person R in 80 % cases. Then the probability that they likely to contradict each other in narr\dots$
17. $If X_{1}, X_{2}, \dots X_{n} are n independent events such that P (X_{r}) \dots$
18. $Three critics review a book. For the three critics the odds in favour of the book are 2 : 5, 3 : 4 and 4 : 3 respectively. The probability that\dots$
19. $If a cubical die is thrown, then the mean and variance of the random variable X, giving the number on the face that shows up, are respectively$
20. $If getting a head on a coin when it is tossed is considered as success, then the probability of having more number of failures when ten fair coins are tossed simultaneous\dots$
21. $Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the bal\dots$
22. $A bag contains 4 red and 6 balck balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour ar\dots$
23. $Two balls are drawn at random from a bag containing 5 black balls and 3 white balls. If the random variable X denotes the number of white balls drawn, then the mean of\dots$
24. $Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such\dots$
25. $A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4 . Then the conditional probability that the score 4 has a\dots$

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Probability: JEE Main Mathematics Previous Year Questions

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