Three numbers are chosen at random without replacement

• Probability

Three numbers are chosen at random without replacement from {1, 2, 3, ...... 8}. The probability that their minimum is 3, given that their maximum is 6, is

1. 2/5
2. 1/4
3. 3/8
4. 1/5

Answer

Let A be the event that maximum is 6.

B be event that minimum is 3

P(A) = ⁵C₂ / ⁸C₃ (the numbers < 6 are 5)

P(B) = ⁵C₂ / ⁸C₃ (the numbers > 3 are 5)

P(A ∩ B) = ²C₁ / ⁸C₃

Required probability is = P(A ∩ B) / P(A)

The correct option is D.