Question

A drawer contains 5 black socks(B), 7 grey socks(G) and 13 white socks(W). Matthew selects two socks from the drawer at random. What is the probability that they are the same color? Give your answer as a decimal correct to three significant figures.

Answer 1

0.363

Explanation:

Number of Black(B) Socks =5

Number of Grey(G) Socks =7

Number of White(W) Socks =13

Total Number of Socks=5+7+13=25

If the two socks are picked one after the other, the total number reduces and the number of that particular color of socks picked also reduces.

To pick the same color, they could either be both black, grey of white.

Therefore:

P(they are of the same color)=P(BB)+P(GG)+P(WW)

`=((5)/(25)X(4)/(24))+((7)/(25)X(6)/(24))+((13)/(25)X(12)/(24))\\=0.363`

The probability that they are of the same color is 0.363 correct to 3 significant figures.