EXPLANATION:
Given;
We are told that Joey's drawer contains the following;
Black dress socks = 3
Black ankle socks = 3
Brown dress socks = 6
Brown ankle socks = 4
Required;
If a sock is chosen at random, find the probability that it is brown or is a dress sock.
Step-by-step solution;
The drawer contains a total of 16 socks.
Also, there is a total of 9 dress socks and 10 brown socks.
The probability of choosing a brown or dress sock will be determined by the following formula;
[tex]P[brown\text{ }sock\text{ }OR\text{ }dress\text{ }sock]=P[brown]+P[dress]-P[brown\text{ }and\text{ }dress][/tex]We can now substitute the values given for this experiment as follows;
[tex]P[brown\text{ }OR\text{ }dress]=\frac{10}{16}+\frac{9}{16}-\frac{6}{16}[/tex][tex]P[brownORdress]=\frac{19}{16}-\frac{6}{16}=\frac{13}{16}[/tex]ANSWER:
The probability that Joey would select a sock at random that is brown or is a dress sock is
[tex]\frac{13}{16}[/tex]Option D is the correct answer.
