A box contains 50 balls, in which 5 are red balls, 6 are green balls,

1.	A box contains 50 balls, in which 5 are red balls, 6 are green balls, 9 are blue balls, and the remaining are yellow balls.Quantity I: Probability of picking 2 balls such that one is green and the other one is blueQuantity II: Probability of picking 3 balls such that at least one of them is redQuantity III: Probability of picking 3 balls such that at least one of them is blue1. Quantity III > Quantity I > Quantity II2. Quantity II > Quantity III > Quantity I3. Quantity III > Quantity II > Quantity I4. Quantity I = Quantity II > Quantity III5. Quantity I > Quantity III < Quantity II
Answer» Correct Answer - Option 3 : Quantity III > Quantity II > Quantity I Quantity I: Probability of picking 2 tiles such that one is green and the other one is blue ⇒ (6 × 9)/⁵⁰C₂ ⇒ 54/(50 × 49/2) ⇒ 54/1225 ⇒ 0.044 Quantity II: Probability of picking 3 balls such that at least one of them is red ⇒ 1 – ⁴⁵C₃/⁵⁰C₃ ⇒ 1 – (45 × 44 × 43/3)/(50 × 49 × 48/3) ⇒ 1 – (14190/19600) ⇒ 541/1960 ⇒ 0.276 Quantity III: Probability of picking 3 balls such that at least one of them is blue ⇒ 1 – ⁴¹C₃/⁵⁰C₃ ⇒ 1 – (41 × 40 × 39/3)/(50 × 49 × 48/3) ⇒ 1 – (10660/19600) ⇒ 894/1960 ⇒ 0.456 Quantity III > Quantity II > Quantity I

A box contains 50 balls, in which 5 are red balls, 6 are green balls, 9 are blue balls, and the remaining are yellow balls.Quantity I: Probability of picking 2 balls such that one is green and the other one is blueQuantity II: Probability of picking 3 balls such that at least one of them is redQuantity III: Probability of picking 3 balls such that at least one of them is blue1. Quantity III > Quantity I > Quantity II2. Quantity II > Quantity III > Quantity I3. Quantity III > Quantity II > Quantity I4. Quantity I = Quantity II > Quantity III5. Quantity I > Quantity III < Quantity II

Answer» Correct Answer - Option 3 : Quantity III > Quantity II > Quantity I

Quantity I:

Probability of picking 2 tiles such that one is green and the other one is blue

⇒ (6 × 9)/⁵⁰C₂

⇒ 54/(50 × 49/2)

⇒ 54/1225

⇒ 0.044

Quantity II:

Probability of picking 3 balls such that at least one of them is red

⇒ 1 – ⁴⁵C₃/⁵⁰C₃

⇒ 1 – (45 × 44 × 43/3)/(50 × 49 × 48/3)

⇒ 1 – (14190/19600)

⇒ 541/1960

⇒ 0.276

Quantity III:

Probability of picking 3 balls such that at least one of them is blue

⇒ 1 – ⁴¹C₃/⁵⁰C₃

⇒ 1 – (41 × 40 × 39/3)/(50 × 49 × 48/3)

⇒ 1 – (10660/19600)

⇒ 894/1960

⇒ 0.456

Quantity III > Quantity II > Quantity I