A box contains 4 white, 5 red, and 6 blue balls. If three balls are drawn at…

2024

A box contains 4 white, 5 red, and 6 blue balls. If three balls are drawn at random from the box, what is the probability that all of them are blue?

  1. A.

    4/91

  2. B.

    4/81

  3. C.

    4/71

  4. D.

    4/61

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Correct answer: A

Step-by-Step Solution

To find the probability of drawing three blue balls, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

  1. Calculate Total Possible Outcomes:

    • Total balls = 4 (white) + 5 (red) + 6 (blue) = 15 balls.

    • The number of ways to choose 3 balls out of 15 is 15C3.

    • 15C3 = (15 * 14 * 13) / (3 * 2 * 1) = 455.

  2. Calculate Favorable Outcomes:

    • We want all three balls to be blue. There are 6 blue balls available.

    • The number of ways to choose 3 blue balls out of 6 is 6C3.

    • 6C3 = (6 * 5 * 4) / (3 * 2 * 1) = 20.

  3. Calculate Probability:

    • Probability = Favorable outcomes / Total outcomes = 20 / 455.

    • Simplifying the fraction by dividing both numerator and denominator by 5:

    • 20 / 5 = 4

    • 455 / 5 = 91

    • The probability is 4/91.

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