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
[tex]^{16}C_2=\dfrac{16!}{2!(16-2)!}=120[/tex]
Total ways to select 2 socks of the same color is
T = Possible ways of (2 blue + 2 white +2 gray) socks
= [tex]^{4}C_2+^{8}C_2+^{4}C_2[/tex]
= [tex]6+28+6[/tex]
= [tex]40[/tex]
The probability of getting 2 socks of the same color is
[tex]Probability=\dfrac{\text{Total ways to select 2 socks of the same color}}{\text{Total ways to select 2 socks form 16 socks}}[/tex]
[tex]Probability=\dfrac{40}{120}[/tex]
[tex]Probability=\dfrac{1}{3}[/tex]
Therefore, the probability of getting 2 socks of the same color is 1/3.
