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Question 45

A box contains 5 brown and 4 white socks. A man takes out two socks. The probability that they are of the same colour is

Solution

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He can pick brown brown Or

brown blue Or

blue blue Or

blue brown

Only the first and third choices are what we want

Brown is $\frac{5/}{9}$ then $\frac{4/}{8}$ as it is not replaced

Blue is $\frac{4/}{9}$ then $\frac{3/}{8}$ same reason

So P(2 brown) $= \frac{5/}{9} \times \frac{4/}{8} = \frac{20/}{72}$

P(2 blue) $= \frac{4/}{9} \times \frac{3/}{8} = \frac{12/}{72}$

P(2 same) $= \frac{20/}{72} + \frac{12/}{72} = \frac{32/}{72} = \frac{4/}{9}$

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