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Probability (Class 12)

JEE Main 2026 (Online) 24th January Morning ShiftMCQEasy📈 Topic in 3% papers+4−1
Ques. 1JEE Main 2026, 24 January (Morning Shift)

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 defective bulbs is

  1. 73108
  2. 67108
  3. 7107
  4. 81108

Answer

(1) 73108

Solution

With replacement, the 8 draws are Bernoulli trials with p = 10100 = 110, q = 910.

P(X 7) = P(X = 7) + P(X = 8)

= 8C7 ( 110 )7 ( 910 ) + ( 110 )8

= 8 9108 + 1108 = 73108

Answer: (1)

Keep practising — Probability (Class 12)

Ques. 2JEE Main 2026, 23 January (Evening Shift)

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 the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is pq, (p, q) = 1, then p + q is equal to

  1. 24
  2. 22
  3. 23
  4. 21
Ques. 3JEE Main 2026, 22 January (Morning Shift)

If a random variable x has the probability distribution arrayccccccccc x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \ P(x) & 0 & 2k & k & 3k & 2k2 & 2k & k2 + k & 7k2 array then P(3 < x 6) is equal to

  1. 0.34
  2. 0.64
  3. 0.22
  4. 0.33
Ques. 4JEE Main 2026, 21 January (Evening Shift)

A random variable X takes values 0, 1, 2, 3 with probabilities 2a+130, 8a-130, 4a+130, b respectively, where a, b R. Let and respectively be the mean and standard deviation of X such that 2 + 2 = 2. Then ab is equal to:

  1. 12
  2. 60
  3. 30
  4. 3
Ques. 5JEE Main 2025, 8 April (Evening Shift)

If A and B are two events such that P(A) = 0.7, P(B) = 0.4 and P(A B) = 0.5, where B denotes the complement of B, then P (B (A B) ) is equal to

  1. 13
  2. 12
  3. 14
  4. 16
Ques. 6JEE Main 2025, 7 April (Evening Shift)

A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is mn, (m, n) = 1, then n2 - m2 is equal to :

  1. 64
  2. 80
  3. 60
  4. 72
Ques. 7JEE Main 2025, 7 April (Evening Shift)

Let a random variable X take values 0, 1, 2, 3 with P(X = 0) = P(X = 1) = p, P(X = 2) = P(X = 3) and E(X2) = 2E(X). Then the value of 8p - 1 is :

  1. 2
  2. 0
  3. 3
  4. 1
Ques. 8JEE Main 2025, 4 April (Morning Shift)

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is

  1. 1115
  2. 215
  3. 35
  4. 2875
Ques. 9JEE Main 2025, 4 April (Evening Shift)

A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is 1150, then n is equal to .

Ques. 10JEE Main 2025, 3 April (Evening Shift)

If the probability that the random variable X takes the value x is given by P(X = x) = k(x + 1)3-x, x = 0, 1, 2, 3, , where k is a constant, then P(X 3) is equal to

  1. 19
  2. 827
  3. 727
  4. 49
Ques. 11JEE Main 2025, 2 April (Evening Shift)

Given three identical bags each containing 10 balls, whose colours are as follows : arraylccc & Red & Blue & Green \ Bag I & 3 & 2 & 5 \ Bag II & 4 & 3 & 3 \ Bag III & 5 & 1 & 4 array A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is q, then the value of ( 1p + 1q ) is:

  1. 6
  2. 9
  3. 7
  4. 8

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