Q59. - Algebra 1

Question

Robert has 30 socks in his sock drawer. 16 of the socks are white, 6 are black, 2 are red, and 6 are yellow. What is the probability that he randomly pulls out a black sock?

Step-by-Step Solution

Answer

The probability of getting a black sock is $\frac{1}{5}$.

Step 1. State the formula.

The probability of an event is the ratio of the number of favorable outcomes to the number of total possible outcomes.

Step 2. List the given data.

There are 30 socks in the drawer; out of which 16 are white socks, 6 are black socks, 2 are red socks and 6 are yellow socks.

Step 3. Calculate the number of favorable and total outcomes.

There are 30 socks in total. So, the total number of outcomes is 30.

The event is “pulling out a black sock”.

There are 6 black socks in the drawer. So, the number of favorable outcomes is 6.

Step 4. Determine the probability.

The probability of pulling out a black sock is the ratio of the number of favorable outcomes to the number of total outcomes.

Then,

$\begin{array}{l}P\left(\text{black sock}\right)=\frac{6}{30}\\ =\frac{1}{5}\end{array}$

So, the probability of pulling out a black sock is $\frac{1}{5}$.