Kevin is trying to find a brown sock in his drawer. He has 16 white socks, 4 brown socks, and 6 black socks. What is the probability that he

Question

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

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Reagan 1 week 2021-09-08T14:40:50+00:00 1 Answer 0

Answers ( )

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    2021-09-08T14:42:17+00:00

    The probability that he pulls out either a black or white sock, puts it back and then pulls out a brown sock is (\frac{22}{169} )

    Step-by-step explanation:

    Here , as given the total number of:

    White Socks  = 16

    Brown Socks = 4

    Black socks  = 6

    So, the total number of socks in the drawer   = 16 + 4 + 6 = 26 socks

    Now, the probability of picking a sock either a black or white sock is

    = \frac{\textrm{Total number of black + white sock}}{\textrm{The total number of socks}}  = \frac{16+6}{26}  = \frac{22}{26}  = \frac{11}{13}

    Also, the picked sock is replaced. So, now the total socks are same = 26.

    the probability of picking a brown sock is

    = \frac{\textrm{Total number of brown sock}}{\textrm{The total number of socks}}  = \frac{4}{26}  = \frac{2}{13}

    Now, since both events are independent events , so the combined probability is given as:

    P (E) = (\frac{11}{13} )\times (\frac{2}{13} ) = (\frac{22}{169} )

    Hence, the probability that he pulls out either a black or white sock, puts it back and then pulls out a brown sock is (\frac{22}{169} )

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