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The numbers 1-10 are placed on cards, and the cards are put in a hat. If two cards are drawn, in order, without replacement, what is the probability that
a. both are composite?
b. one number is even and the other is odd?
c. one number is even and the other a prime?

  • Math -

    a) composites are 6,8,9, and 10
    prob(both composites) = C(4,2)/C(10,2) = 6/45 = 2/15

    b) prob(one even and one odd) = C(5,1)C(5,1)/C(10,2)
    = 25/45 = 5/9

    4 primes: 2,3,5,7
    5 even:2,4,6,8,10

    prob(one even and the other odd)
    Case 1: the 2 is in there
    number of ways for the other number is 3
    Case 2: the 2 is out
    number of ways is 3x4 = 12
    total is 15
    prob(one even the other prime) = 15/45 = 1/3

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