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Probability (Class 12) · Question 1

JEE Main 2026 (Online) 8th April Evening ShiftMCQEasy📈 Topic in 23% papers+4−1
1

A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are 25, 15 and 25. The probabilities that the candidate reaches late at the examination centre are 15, 13 and 14 if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is :

  1. 1137
  2. 1237
  3. 1337
  4. 1437

Answer

(2) 1237

Solution

Let B, S, C: the candidate goes by bus, scooter, car; L: the candidate reaches late

P(B)= 25, P(S)= 15, P(C)= 25; P(L|B)= 15, P(L|S)= 13, P(L|C)= 14

Total probability: P(L)= 25 15+ 15 13+ 25 14

= 225+ 115+ 110= 12+10+15150= 37150

Bayes' theorem: P(B|L)= P(B)P(L|B)P(L)= 12/15037/150= 1237

Answer: (2)

JEE Main 2026 (Online) 8th April Evening Shift

Keep practising — Probability (Class 12)

2

A bag contains (N+1) coins - N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is 916, then N is equal to :

  1. 5
  2. 7
  3. 8
  4. 9
JEE Main 2026 (Online) 6th April Morning Shift
3

A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:

  1. 710
  2. 1017
  3. 1219
  4. 719
JEE Main 2026 (Online) 5th April Morning Shift
4

The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4, respectively. If A is selected the captain, the probability that the team wins the tournament is 0.8 and if B is selected the captain, the probability that the team wins the tournament is 0.7. Then the probability, that the team wins the tournament, is :

  1. 0.74
  2. 0.76
  3. 0.72
  4. 0.78
JEE Main 2026 (Online) 5th April Evening Shift
5

A bag contains 10 balls out of which k are red and (10 − k) are black, where 0 k 10. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:

  1. 7110
  2. 711
  3. 755
  4. 1455
JEE Main 2026 (Online) 28th January Morning Shift
6

The probability distribution of a random variable X is given below : array|c|c|c|c|c|c|c|c|c| X & 4k & 307k & 327k & 347k & 367k & 387k & 407k & 6k \ P(X) & 215 & 115 & 215 & 15 & 115 & 215 & 15 & 115 \ array If E(X) = 26315, then P(X < 20) is equal to :

  1. 35
  2. 1415
  3. 815
  4. 1115
JEE Main 2026 (Online) 28th January Evening Shift
7

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
JEE Main 2026 (Online) 24th January Morning Shift
8

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
JEE Main 2026 (Online) 23rd January Evening Shift
9

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
JEE Main 2026 (Online) 22nd January Morning Shift
10

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
JEE Main 2026 (Online) 21st January Evening Shift
11

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
JEE Main 2025 (Online) 8th April Evening Shift

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