Multiple choice

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn is

  1. $\dfrac {40}{143}$
  2. $\dfrac {70}{143}$
  3. $\dfrac {3}{13}$
  4. $\dfrac {10}{13}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total balls = 13. Total ways to draw 3 balls = 13C3 = (13*12*11)/(3*2*1) = 286. Ways to draw only red = 8C3 = 56. Ways to draw only white = 5C3 = 10. Ways to draw both colors = Total - (only red + only white) = 286 - (56 + 10) = 220. Probability = 220/286 = 110/143 = 10/13.

AI explanation

The total number of balls is 8 red + 5 white = 13 balls, so the total ways to draw 3 balls is (13 choose 3) = 286. The probability of drawing both colors is 1 minus the probability of drawing only red balls (8 choose 3 = 56) minus the probability of drawing only white balls (5 choose 3 = 10). This gives 1 minus (56/286) minus (10/286), which equals 220/286 and simplifies to 10/13.

Keep practicing — related questions