An urn contains 2 small pink balls, 7 small purple balls, and 6 small white balls. Three balls are selected, one after the other, with

Question

An urn contains 2 small pink balls, 7 small purple balls, and 6 small white balls.
Three balls are selected, one after the other, without replacement.
Find the probability that all three balls are purple
Express your answer as a decimal, rounded to the nearest hundredth.

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Thu Thủy 3 years 2021-07-23T18:39:58+00:00 1 Answers 24 views 0

Answers ( )

  1. thuthao
    0
    2021-07-23T18:41:37+00:00
    Reply

    Answer:

    The probability is P = 0.08

    Step-by-step explanation:

    We have:

    2 pink balls

    7 purple balls

    6 white balls

    So the total number of balls is just:

    2 + 7 + 6 = 15

    We want to find the probability of randomly picking 3 purple balls (without replacement).

    For the first pick:

    Here all the balls have the same probability of being drawn from the urn, so the probability of getting a purple one is equal to the quotient between the number of purple balls (7) and the total number of balls (15)

    p₁ = 7/15

    Second:

    Same as before, notice that because the balls are not replaced, now there are 6 purple balls in the urn, and a total of 14 balls, so in this case the probability is:

    p₂ = 6/14

    third:

    Same as before, this time there are 5 purple balls in the urn and 13 balls in total, so here the probability is:

    p₃ = 5/13

    The joint probability (the probability of these 3 events happening) is equal to the product between the individual probabilities, so we have:

    P = p₁*p₂*p₃ = (7/15)*(6/14)*(5/13)  = 0.08

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