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

Answer:

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

Step-by-step 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

$^{16}C_2=\dfrac{16!}{2!(16-2)!}=120$

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

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

$Probability=\dfrac{40}{120}$

$Probability=\dfrac{1}{3}$

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