Question

a sock drawer contains 5 different colors of socks. it has 20 white, 10 black, 10 gray, 6 red, and 4 purple. if you reach into the drawer and choose a sock randomly, what is the probability you will get a black sock? (write your final answer as a fraction.)

$p(\text{black}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$

$p(\text{black}) = \square$

Explanation:

Step1: Calculate total number of socks

We sum up the number of socks of each color: \(20 + 10 + 10 + 6 + 4\)
\(20+10 = 30\), \(30+10 = 40\), \(40+6 = 46\), \(46+4 = 50\). So total number of socks is \(50\).

Step2: Determine number of black socks

The number of black socks is \(10\).

Step3: Calculate probability of black sock

Using the formula \(P(\text{black})=\frac{\text{Number of black socks}}{\text{Total number of socks}}\), we substitute the values: \(\frac{10}{50}\), which simplifies to \(\frac{1}{5}\) (dividing numerator and denominator by 10).

Answer:

\(\frac{1}{5}\)