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5 February, 05:31

A bowl contains 10 chips, of which 8 are marked $2 each and 2 are marked $5 each. Let a person choose, at random and without replacement, three chips from this bowl. If the person is to receive the sum of the resulting amounts, find his expectation.

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  1. 5 February, 05:39
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    Answer:$7.8

    Step-by-step explanation:

    We have three cases to this question which are;

    (a). Getting two $2 and one $5

    (b). Getting one $2 and two $5

    (c). Getting all three $2

    Note: there are 10:3 ways of doing this.

    Computing the probability of each, we have:

    (a). We have {8; 2} {2; 1} ways to get two $2. Therefore, the probability gives;

    (8; 2) (2; 1) : 10; 3) we get 9 here.

    (b). (8; 1) (2; 2) : (10; 3)

    We have 12 here.

    (c). (8; 3) (2; 0) : (10; 3) = 6

    The expectation;

    (10; 3) = 120, (8; 3) (2; 0) = 56.

    (8; 2) (2; 1) = 56 and (8; 1) (2; 2) = 8.

    So, the expectation is;

    9.56+12.8+6.56:120

    = 936:120

    = 39:5

    = $7.8.
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