Question

1. donatos little brother joseph is too small to see inside his sock drawer. joseph has 2 pairs of white socks, 4 pairs of black socks, and 1 pair of blue socks inside his drawer. if the socks are not paired together, what is the probability that joseph will reach inside his drawer and pick a black sock?

a $\frac{2}{7}$ b $\frac{3}{7}$ c $\frac{4}{7}$ d $\frac{6}{7}$

Explanation:

Step1: Calculate total number of socks

First, find the total number of individual socks. Each pair has 2 socks:
White socks: $2 \times 2 = 4$
Black socks: $4 \times 2 = 8$
Blue socks: $1 \times 2 = 2$
Total socks: $4 + 8 + 2 = 14$

Step2: Calculate probability of black sock

Probability is the number of favorable outcomes (black socks) divided by total outcomes (total socks):
$\text{Probability} = \frac{\text{Number of black socks}}{\text{Total number of socks}} = \frac{8}{14} = \frac{4}{7}$

Answer:

[C] $\frac{4}{7}$