Question

Joey’s sock drawer is unorganized and contains 3 black dress socks, 3 black ankle socks, 6 brown dress socks, and 4 brown ankle socks. What is the probability that Joey chooses a sock at random that is brown or is a dress sock?A) 1, or 100%B) 19/16C) 3/8D) 13/16

Answer 1

Step-by-step 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;

`P[brown\text{ }sock\text{ }OR\text{ }dress\text{ }sock]=P[brown]+P[dress]-P[brown\text{ }and\text{ }dress]`

We can now substitute the values given for this experiment as follows;

`P[brown\text{ }OR\text{ }dress]=(10)/(16)+(9)/(16)-(6)/(16)`
`P[brownORdress]=(19)/(16)-(6)/(16)=(13)/(16)`

ANSWER:

The probability that Joey would select a sock at random that is brown or is a dress sock is

`(13)/(16)`

Option D is the correct answer.