Probability I, Solved Paper Question: Jee 1 year MATH, Math - Meritnation

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Probability - I

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 results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2, 3, ..., 9 is randomly picked and the number on the card in noted. The probability that the noted number is either 7 or 8 is:

JEE Mains 2019

Let S = {1, 2, ..., 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is "nice" is:

JEE Mains 2019

If the probability of hitting a target by a shooter, in any shot, is

\frac{1}{3}

, then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than

\frac{5}{6}

JEE Mains 2019

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 probability that the student selected has opted neither for NCC nor for NSS is:

JEE Mains 2019

If two different numbers are taken from the set {0, 1, 2, 3,....., 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is

JEE Mains 2017

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

JEE Advanced 2017

If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :

JEE Mains 2015

Let A and B be two events such that

P (A \cup B) = \frac{1}{6}, P (A \cap B) = \frac{1}{4} and P (A) = \frac{1}{4},

A

stands for the complement of the event A. Then the events A and B are

JEE Mains 2014

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

JEE Advanced 2014

Box 1 contains three cards bearing numbers 1, 2 and 3; box 2 contains five cards bearing numbers 1, 2, 3, 4 and 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6 and 7. A card is drawn from each of the boxes. Let x_i be the number on the card drawn from the i^th box, i = 1, 2, 3.
The probability that x₁ + x₂ + x₃ is odd is

JEE Advanced 2014

The probability that x₁, x₂ and x₃ are in arithmetic progression is

JEE Advanced 2014

Four fair dice and, each having six faces numbered 1, 2,3,4,5 and 6, are rolled simultaneously. The probability that shows a number appearing on one of and is

JEE Advanced 2012

Let be a complex cube root of unity with. A fair die is thrown three times. If r₁, r₂and r₃are the numbers obtained on the die, then theprobability that is

JEE 2010

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