A bag contains `5` brown and `4` white socks. A man pulls out two socks. The probability that these are of the same colour is

Options

A. a) `5/(108)`
B. b) `(18)/(108)`
C. c) `(31)/(108)`
D. d) `(48)/(108)`

Answer

d) `(48)/(108)`

Explanation

Total sample space of socks `=9` (4B,5W)


Probability `=P(B,B)` or `P(W,W)`


`=P(B)*P(B)+P(W)*P(W)`


Probability of brown socks in 1st draw `=4/9`


Probability of brown socks in 2nd draw `=3/8` (without replacement)


Probability of white socks in 1st draw `=5/9`


Probability of white socks in 2nd draw `=4/8` (without replacement)


Required probability `=4/9*3/8+5/9*4/8`


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