Multiple choice

In the given questions, two quantities are given, one as Quantity I and another as Quantity II. You have to determine relationship between two quantities and choose the appropriate option. A box contains 4 Red balls, 6 white balls, 2 orange balls and 8 black balls. Quantity I: Two balls are drawn at random probability that both balls are either red or white. Quantity II: Three balls are drawn. The probability that all are different.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total balls = 4+6+2+8 = 20. Quantity I: P(2 Red or 2 White) = (4C2 + 6C2) / 20C2 = (6 + 15) / 190 = 21/190 approx 0.11. Quantity II: P(3 different) = (4*6*2 + 4*6*8 + 4*2*8 + 6*2*8) / 20C3 = (48 + 192 + 64 + 96) / 1140 = 400/1140 approx 0.35. Thus, I < II.

AI explanation

The box has a total of 20 balls, so Quantity I is the sum of choosing 2 red from 4 and 2 white from 6, divided by choosing 2 from 20, which equals 21/95. For Quantity II, drawing three different colored balls can be done in 4 times 6 times 2, plus 4 times 6 times 8, plus 4 times 2 times 8, plus 6 times 2 times 8 ways, totaling 368 favorable outcomes out of 1140, which is 92/285. Comparing 21/95 to 92/285 by converting to a common denominator gives 63/285 and 92/285, showing that Quantity I is less than Quantity II.

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