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A bowl contains 16 marbles of three colors, 6 red, 4 blue and rest of purple. Three marbles are drawn one by one and not replaced. What is probability that the marbles drawn are of three different colors and first being red color?

A bowl contains 16 marbles of three colors, 6 red, 4 blue and rest of purple. Three marbles are drawn one by one and not replaced. What is probability that the marbles drawn are of three different colors and first being red color? Correct Answer 3 / 35

Given:

16 marbles = 6 red + 4 blue + 6 purple

Calculation:

There are two options in this scenario

⇒ Case 1 = Red, Blue, Purple would be drawn out

⇒ Case 2 = Red, Purple, Blue would be drawn out

⇒ Probability in case 1 = (6 / 16) × (4 / 15) × (6 / 14)

⇒ Probability in case 2 = (6 / 16) × (6 / 15) × (4 / 14)

⇒ Probability = ((6 / 16) × (4 / 15) × (6 / 14)) + ((6 / 16) × (4 / 15) × (6 / 14))

⇒ Probability = 2 × (6 × 4 × 6) / (16 × 15 × 14)

⇒ Probability = 2 × 18 / 420

⇒ Probability = 3 / 35

∴ Probability of drawing out three different marbles of different colors with first being red is 3 / 35

Hint

Find probability of any one arrangement first and double it up seeing numerators and denominators remain the same

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