Multiple choice

A bag contains $8$ white and $6$ red balls. $5$ balls are drawn from the bag at random. The probability that $3$ or more balls are white will be -

  1. $658/1001$
  2. $318/1001$
  3. $205/1001$
  4. $210/1001$
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A Correct answer
Explanation

Total balls = 14. We choose 5. The number of ways to choose 3 white (from 8) and 2 red (from 6) is C(8,3)*C(6,2) = 56*15 = 840. The ways to choose 4 white and 1 red is C(8,4)*C(6,1) = 70*6 = 420. The ways to choose 5 white is C(8,5) = 56. Total favorable outcomes = 840 + 420 + 56 = 1316. Total possible outcomes = C(14,5) = 2002. Probability = 1316/2002 = 658/1001.

AI explanation

The total number of ways to draw 5 balls from 14 is 14C5 = 2002, making the denominator for our probabilities 2002. We calculate the probability of getting exactly 3, 4, or 5 white balls by finding the sum of (8C3 * 6C2) + (8C4 * 6C1) + (8C5 * 6C0), which equals 840 + 420 + 56 = 1316. Dividing this sum by 2002 gives 1316/2002, which simplifies to 658/1001.

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