Multiple choice

Passage

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities.

In a bag, there are 5 black, 3 green and 4 red balls. 3 balls are picked at random. Quantity I: The probability that 2 balls are green in colour and 1 ball is red in colour. Quantity II: The probability that all the balls are black in colour.

  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
C Correct answer
Explanation

Total balls = 12. Quantity I: P(2G, 1R) = (3C2 * 4C1) / 12C3 = (3 * 4) / 220 = 12/220. Quantity II: P(3B) = 5C3 / 12C3 = 10 / 220. Since 12/220 > 10/220, I > II.

AI explanation

The total number of balls in the bag is 12, so the total number of ways to pick 3 balls is 12C3, which equals 220. For Quantity I, the number of ways to pick 2 green and 1 red ball is 3C2 times 4C1, which is 3 times 4 to equal 12, making the probability 12/220 or 3/55. For Quantity II, the number of ways to pick 3 black balls is 5C3, which equals 10, making the probability 10/220 or 1/22. Comparing the two values, 3/55 is greater than 1/22, so Quantity I > Quantity II.

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