Question

of the 528 clients at bernies salon, 122 of them have black hair.
what is the probability that a randomly selected client at bernies salon has black hair?
write your answer as a fraction or whole number.
p(black) =

Explanation:

Step1: Recall the probability formula

Probability \( P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Here, the number of favorable outcomes (clients with black hair) is \( 122 \), and the total number of outcomes (total clients) is \( 528 \). So, \( P(\text{black})=\frac{122}{528} \).

Step2: Simplify the fraction

Find the greatest common divisor (GCD) of \( 122 \) and \( 528 \). The factors of \( 122 \) are \( 1,2,61,122 \), and the factors of \( 528 \) are \( 1,2,3,4,6,8,11,12,16,22,24,33,44,48,66,88,132,176,264,528 \). The GCD of \( 122 \) and \( 528 \) is \( 2 \). Divide both numerator and denominator by \( 2 \): \( \frac{122\div2}{528\div2}=\frac{61}{264} \).

Answer:

\( \frac{61}{264} \)