Statistics/Probability

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The probability the New Year's day is on Saturday is a randomly chosen year is 1/7.
15 years was chosen randomly. Find the probability that,
(1) Exactly four of these years have a New Year's day on a Saturday.
(2) At least two of these years have New Year's day on a Saturday.

  • Statistics/Probability -

    prob(Saturday) = 1/7
    prob(not Saturday) = 6/7

    prob(exactly 4 of 15 years is a Saturday)
    = C(15,4) (1/7)^4 (6/7)^11
    = appr .1043

    at least 2 Saturdays ----> 1 - (case of 0 Saturday + case of 1 Saturday)
    = 1 - (6/7)^15 - C(15,1)(1/7)(6/7)^14
    = .6534

    check my arithmetic

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