probability

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A box contains 4 red and 3 blue poker chips. What is the probability when 3 are selected randomly that all 3 wil be red if we select chips with replacement?


a.) Without replacement?

  • probability -

    To get one red out of the seven, you have 4 chances, so the probability is
    4/7.
    Since the chips will be replaced, the second and subsequent draws will be under the same conditions, i.e. they are independent. The probability of each subsequent draw is again 4/7.
    The probability of joint independent events is the product of the individual probabilities, thus
    in this case,
    (4/7)*(4/7)*(4/7)=?

    Without replacement, after each successful draw, there will be one red chip less.
    Probability for first draw:
    4/7 as before
    second draw:
    3/6
    third draw:
    2/5
    So probability of all three events happening:
    (4/7)*(3/6)*(2/5)
    =4/35

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