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18 July, 20:27

You are packing clothes for vacation and don't want to take any button-down shirts. You randomly choose 3 shirts from a drawer containing 3 t-shirts, 3 polo shirts, and 4 button-downs. (put both answers in as a reduced fraction)

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  1. 18 July, 22:56
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    a) P = 64/1000 = 0.064

    b) P = 1/30 = 0.033

    Completed question:

    You are packing clothes for vacation and don't want to take any button-down shirts. You randomly choose 3 shirts from a drawer containing 3 t-shirts, 3 polo shirts, and 4 button-downs. (put both answers in as a reduced fraction)

    a. What is the probability that the first 3 shirts are button-downs when you replace each shirt before choosing the next one?

    b. What is the probability that the first 3 shirts are button-downs when you do not replace each shirt before choosing the next one?

    Step-by-step explanation:

    Given;

    Number of T-shirts = 3

    Number of Polo shirts = 3

    Number of button-downs = 4

    Total number of shirts = 3+3+4 = 10

    Number of shirts to be selected = 3

    a) with replacement

    probability P that the first 3 shirts are button-downs is;

    P = 4/10 * 4/10 * 4/10

    P = 64/1000 = 0.064

    b) without replacement

    probability P that the first 3 shirts are button-downs is;

    P = 4/10 * 3/9 * 2/8

    P = 24/720 = 1/30

    P = 1/30 = 0.033
  2. 19 July, 00:15
    0
    Complete Question:

    You are packing clothes for vacation and don't want to take any button-down shirts. You randomly choose 3 shirts from a drawer containing 3 t-shirts, 3 polo shirts, and 4 button-downs. (put both answers in as a reduced fraction)

    a. What is the probability that the first 3 shirts are button-downs when you replace each shirt before choosing the next one?

    b. What is the probability that the first 3 shirts are button-downs when you do not replace each shirt before choosing the next one?

    Answer:

    a) Probability of selecting 3 button down shirts with replacement = 0.064

    b) Probability of selecting three button down shirts without replacement = 0.033

    Step-by-step explanation:

    The total number of shirts = 3 t shirts + 3 polo shirts + 4 button - downs

    The total number of shirts = 10

    a) Three button down shirts are selected with replacement

    Number of button down shirts available = 4

    Probability of selecting a button down shirt = 4/10 = 0.4

    Probability of selecting 3 button down shirts with replacement = 0.4 * 0.4 * 0.4 = 0.064

    b) Probability of selecting three button down shirts without replacement

    Probability of selecting the first button down shirt = 4/10 = 0.4

    Probability of selecting the second button down shirt = 3/9 = 0.33

    Probability of selecting the third button down shirt = 2/8 = 0.25

    Probability of selecting three button down shirts without replacement = 0.4 * 0.33 * 0.25 = 0.033
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