Multiple choice

A box contains 4 Red balls, 3 white balls, 5 orange balls and 6 blue balls. Quantity I: If two balls are drawn at random, then find the probability that both the balls are either orange or blue? Quantity II: If four balls are drawn at random, then find the probability that all the balls are different in colour?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
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A Correct answer
Explanation

Total balls = 4+3+5+6 = 18. Quantity I: P(2 orange or 2 blue) = (5C2 + 6C2) / 18C2 = (10 + 15) / 153 = 25/153 approx 0.163. Quantity II: P(4 different) = (4C1 * 3C1 * 5C1 * 6C1) / 18C4 = (4*3*5*6) / 3060 = 360 / 3060 approx 0.117. Quantity I > Quantity II.

AI explanation

For Quantity I, the total balls are 18, and the probability of drawing two orange or two blue balls is the sum of their individual combinations divided by the total combinations: 5C2 plus 6C2 gives 10 plus 15 equals 25, and 18C2 equals 153, making the probability 25 divided by 153. For Quantity II, the probability of drawing four different colored balls is the product of the counts divided by the total combinations: 4 times 3 times 5 times 6 equals 360, and 18C4 equals 3060, making the probability 360 divided by 3060, which simplifies to 2 divided by 17. Comparing 25 divided by 153 to 18 divided by 153, Quantity I is greater.

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