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Probability · Question 8

JEE Main 2026 (Online) 22nd January Morning ShiftMCQEasy📈 Topic in 39% papers+4−1
1

Two distinct numbers a and b are selected at random from 1, 2, 3, , 50. The probability, that their product ab is divisible by 3, is

  1. 2721225
  2. 5611225
  3. 6641225
  4. 825

Answer

(3) 6641225

Solution

Total ways = 50C2 = 50 492 = 1225

Multiples of 3 in 1 to 50: 3, 6, , 48 → 16 numbers

Non-multiples = 50 - 16 = 34

ab is not divisible by 3 both are non-multiples:

ways = 34C2 = 34 332 = 561

P(ab divisible by 3) = 1 - 5611225 = 6641225

Answer: (3)

JEE Main 2026 (Online) 22nd January Morning Shift

Keep practising — Probability

2

The probability of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is

  1. 129182
  2. 1726
  3. 1926
  4. 103182
JEE Main 2025 (Online) 4th April Morning Shift
3

Three distinct numbers are selected randomly from the set \1, 2, 3, , 40\. If the probability, that the selected numbers are in an increasing G.P., is mn, (m, n) = 1, then m + n is equal to .

JEE Main 2025 (Online) 2nd April Morning Shift
4

Two numbers k1 and k2 are randomly chosen from the set of natural numbers. Then, the probability that the value of ik1 + ik2, (i = -1) is non-zero, equals

  1. 34
  2. 12
  3. 14
  4. 23
JEE Main 2025 (Online) 28th January Morning Shift
5

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:

  1. 14
  2. 12
  3. 13
  4. 23
JEE Main 2025 (Online) 28th January Evening Shift

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All JEE Main Mathematics chapters
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