March 29, 2017

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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
    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,

    Without replacement, after each successful draw, there will be one red chip less.
    Probability for first draw:
    4/7 as before
    second draw:
    third draw:
    So probability of all three events happening:

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