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

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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