JEE Main202125 Jul 2021Morning ShiftMathematicsProbabilityActual
Let 9 distinct balls be distributed among 4 boxes, B 1 , B 2 , B 3 and B 4 . If the probability that B 3 contains exactly 3 balls is k 3 4 9 then k lies in the set :
Options
- Ax ∈ R : | x - 3 | < 1
- Bx ∈ R : | x - 2 | ≤ 1
- Cx ∈ R : | x - 1 | < 1
- Dx ∈ R : | x - 5 | ≤ 1
Correct answer
A. x ∈ R : | x - 3 | < 1
Step-by-step solution
The number of ways in which 9 distinct balls can be distributed among 4 boxes is 4 9 The number of ways in which B 3 contains 3 balls is C 3 9 · 3 6 Using the classical definition of probability we can say the required probability = C 3 9 · 3 6 4 9 = C 3 9 27 · 3 4 9 = 28 9 · 3 4 9 ⇒ k = 28 9 ≈ 3 . 11 Now, consider | x - 3 | < 1 ⇒ - 1 < x - 3 < 1 ⇒ - 1 + 3 < x < 1 + 3 ⇒ 2 < x < 4 ∴ k satisfies | x - 3 | < 1