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29 September, 07:24

A drawer contains 8 white and 2 black socks. two socks are randomly selected from the drawer. what is the probability they are the same color?

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  1. 29 September, 07:30
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    You can draw a probability tree to work thus out.

    First work out the probability for getting 2 whites in a row.

    It is the number of whites divided by the overall number of socks so 8/10.

    Then, work the probability of doing it for a second time. This is 7/9 since you took away a sock.

    Now multiply 8/10 x 7/9 so 56/90.

    56/90 is the probability of getting two whites in a row, but you now need to work out the probability of two blacks.

    By the same process, you can work out that the calculation is 2/10 x 1/9, so 2/90.

    To work out the total probability of two of the same colour, you add the probabilities of 2 whites and 2 blacks, so it is 56/90 + 2/90, so 58/90, which can be simplified to 29/45.

    Your final answer is 29/45.
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