Question

Deena has 4
pairs of white socks, 3
pairs of black socks, 1
pair of red socks, and 2
pairs of navy socks in her sock drawer. Each pair of socks is folded together. If she pulls a pair of socks out of her drawer in the morning without looking, what is the probability that she will choose a pair of navy socks?

Answer 1

To find the probability that Deena will choose a pair of navy socks, we first need to determine the total number of pairs of socks in her drawer.

**Step 1: Calculate the total number of pairs of socks.**

- White socks: 4 pairs
- Black socks: 3 pairs
- Red socks: 1 pair
- Navy socks: 2 pairs

Now, we can sum these:

\[
\text{Total pairs} = 4 + 3 + 1 + 2 = 10 \text{ pairs}
\]

**Step 2: Determine the number of favorable outcomes for choosing navy socks.**

There are 2 pairs of navy socks.

**Step 3: Calculate the probability.**

The probability \( P \) of choosing a pair of navy socks is given by the ratio of the number of favorable outcomes to the total number of outcomes:

\[
P(\text{navy socks}) = \frac{\text{Number of navy pairs}}{\text{Total pairs}} = \frac{2}{10} = \frac{1}{5}
\]

Thus, the probability that Deena will choose a pair of navy socks is \( \frac{1}{5} \).