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21 December, 10:50

A box contains 7 yellow, 5 blue, and 4 red balls. Three balls are drawn at random. Find the probability that:

a)

All three balls are the same color

c)

Two balls are yellow and one is blue

d)

All three balls are different colors

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Answers (1)
  1. 21 December, 11:19
    0
    a) 7/80 = 0.0875

    b) 3/16 = 0.1875

    c) 1/4 = 0.2500

    Step-by-step explanation:

    There are a total of 16 balls. 3 are selected. There are ₁₆C₃ possible combinations.

    a) If all 3 balls are the same color, they are either all yellow OR all blue OR all red.

    The number of ways of choosing 3 yellow balls from 7 is ₇C₃.

    The number of ways of choosing 3 blue balls from 5 is ₅C₃.

    The number of ways of choosing 3 red balls from 4 is ₄C₃.

    The total probability is:

    P = (₇C₃ + ₅C₃ + ₄C₃) / ₁₆C₃

    P = (35 + 10 + 4) / 560

    P = 49 / 560

    P = 7 / 80

    P = 0.0875

    b) The number of ways of choosing 2 yellow balls from 7 is ₇C₂.

    The number of ways of choosing 1 blue ball from 5 is ₅C₁.

    The probability of both is:

    P = ₇C₂ ₅C₁ / ₁₆C₃

    P = 21 * 5 / 560

    P = 105 / 560

    P = 3 / 16

    P = 0.1875

    c) If all 3 balls are different colors, then there is exactly 1 yellow, 1 blue, and 1 red.

    The number of ways of choosing 1 yellow ball from 7 is ₇C₁.

    The number of ways of choosing 1 blue ball from 5 is ₅C₁.

    The number of ways of choosing 1 red ball from 4 is ₄C₁.

    The probability of all events is:

    P = ₇C₁ ₅C₁ ₄C₁ / ₁₆C₃

    P = 7 * 5 * 4 / 560

    P = 140 / 560

    P = 1 / 4

    P = 0.2500
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