Question

A sock drawer has three colors of socks: white, brown, and black. If the probability of getting a black sock is 7/12 and the probability of getting a white sock is 1/4, what is the probability of getting a brown sock?

Answer 1

A sock drawer has three colors of socks: white, brown, and black

The probability of getting a black sock = 7/12

The probability of getting a white sock = 1/4

The probability of getting a brown sock = ?

Recall that the sum of all probabilities must be equal to 1

So, we can write

`P(white)+P(black)+P(brown)=1`

Substitute the given probabilities and solve for P(brown)

`\begin{gathered} P(white)+P(black)+P(brown)=1 \\ (1)/(4)+(7)/(12)+P(brown)=1 \\ P(brown)=1-(1)/(4)-(7)/(12) \\ P(brown)=(1)/(6) \end{gathered}`

Therefore, the probability of getting a brown sock is 1/6

Option D is the correct answer.