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13 January, 03:37

Kevin is trying to find a white sock in his drawer. He has 16 white socks, 4 brown socks, and 6 black socks. What is the probability that he pull out either a black or brown sock, puts it back, and then pulls out a white sock?

A) 9/13

B) 20/13

C) 40/169

D) 96/169

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  1. 13 January, 04:05
    0
    We have to assume that he does all this with his eyes closed, and so his selections are completely random.

    - - There are 26 socks in the drawer all together.

    - - 10 of them are black or brown.

    - - So the probability that he pulls out

    either a black sock or a brown one is

    10/26 = 5/13 = about 38.5%.

    - - He puts it back, so there are still 26 socks in the drawer.

    - - 16 of them are white.

    - - So now, the probability of pulling out a white one is

    16/26 = 8/13 = about 61.5%.

    The probability of the whole process happening

    just exactly as you described it is

    (10/26) x (16/26)

    = (5/13) x (8/13)

    = (40) / (13²) = 40/169 = about 23.7%.

    Quick check:

    We got 38.5% the first time, and 61.5% the second time.

    (38.5%) x (61.5%)

    = (0.385 x 0.615)

    = 0.2367 = = > 23.7% < = = yay! that's good enough for me
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