Three distinct integers are chosen at random from the first 20 positive integers. Compute the probability that: (a) their sum is even; (b) t

Question

Three distinct integers are chosen at random from the first 20 positive integers. Compute the probability that: (a) their sum is even; (b) their product is even.

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Brielle 2 weeks 2022-01-10T20:33:54+00:00 1 Answer 0 views 0

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    2022-01-10T20:35:37+00:00

    Answer:

    Step-by-step explanation:

    There are first 20 positive integers 1,2…20. Three distinct integers are chosen at random.

    Total no of ways of drawing 3 integers = 20C3 = 1140

    To  Compute the probability that: (a) their sum is even

    a) Sum can be even if either all 3 are even or 1 is even and 2 are odd.

    There are in total 10 odd and 10 even.

    Ways of sum even = 10C3 + 10C2 (10C1)\\= 120+45(10)\\= 570

    Prob = \frac{570}{1140} =0.50

    b) their product is even

    Here any one should be even or both

    SO no of ways are

    =10C2 +10C2(10C1)\\= 45 +450\\=495

    Prob = \frac{495}{1140} =0.4342

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45:7+7-4:2-5:5*4+35:2 =? ( )