Multiple choice

A bag contains 5 Red , 3 Blue and 4 Black balls. 3 balls are drawn randomly then what is the probability getting exactly one balls is red?

  1. $2/5$
  2. $1/132$
  3. $2/33$
  4. $21/44$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total balls = 5R + 3B + 4Black = 12. We need exactly 1 red in 3 draws. Number of ways to choose 1 red from 5 and 2 non-red from 7 = C(5,1) × C(7,2) = 5 × 21 = 105. Total ways to choose any 3 balls from 12 = C(12,3) = 220. Probability = 105/220 = 21/44 after dividing by 5. The calculation 105/220 simplifies to 21/44.