Question

Mixed in a drawer are 44 blue​ socks, 88 white​ socks, and 44 gray socks. You pull out two​ socks, one at a​ time, without looking. Find the probability of getting 2 socks of the same color.

Answer 1

The probability of getting 2 socks of the same color is 1/3.

Explanation:

In the drawer,

Number of blue socks = 4

Number of white socks = 8

Number of gray socks = 4

Total number of socks = 4 + 8 + 4 = 16

Total ways to select 2 socks form 16 socks is

`^(16)C_2=(16!)/(2!(16-2)!)=120`

Total ways to select 2 socks of the same color is

T = Possible ways of (2 blue + 2 white +2 gray) socks

=
`^(4)C_2+^(8)C_2+^(4)C_2`

=
`6+28+6`

=
`40`

The probability of getting 2 socks of the same color is

`Probability=\frac{\text{Total ways to select 2 socks of the same color}}{\text{Total ways to select 2 socks form 16 socks}}`

`Probability=(40)/(120)`

`Probability=(1)/(3)`

Therefore, the probability of getting 2 socks of the same color is 1/3.