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? options: \\(\frac{1}{4}\\), \\(\frac{2}{3}\\), \\(\frac{3}{5}\\), \\(\frac{1}{5}\\)

Explanation:

Step1: Calculate total number of sock pairs

We add the number of pairs of each color: white (4) + black (3) + red (1) + navy (2). So total pairs $n = 4 + 3 + 1 + 2 = 10$.

Step2: Calculate probability of choosing navy socks

The number of navy sock pairs is 2. Probability $P$ is the number of favorable outcomes (navy pairs) divided by total outcomes (total pairs). So $P=\frac{2}{10}=\frac{1}{5}$. Wait, but let's check again. Wait, 4 (white) + 3 (black) is 7, plus 1 (red) is 8, plus 2 (navy) is 10. Favorable is 2. So $\frac{2}{10}=\frac{1}{5}$? Wait, but the options have 1/5 as one of them? Wait the options are 1/4, 2/3, 3/5, 1/5. Wait, maybe I miscalculated total? Wait 4 white, 3 black, 1 red, 2 navy. 4+3=7, 7+1=8, 8+2=10. Yes. So favorable is 2, total 10. So 2/10=1/5. So the probability is 1/5.

Answer:

$\frac{1}{5}$ (corresponding to the option with $\frac{1}{5}$)