Question

1. your sock drawer has four white socks, four brown socks, and six black socks. you randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. you leave the house with a white sock on your left foot and a brown sock on your right foot.

Explanation:

Step1: Calculate total number of socks

There are \(4\) white socks, \(4\) brown socks and \(6\) black socks. So the total number of socks is \(4 + 4+6=14\) socks.

Step2: Calculate probability of first - pick

The probability of picking a white sock for the left - foot first. The number of white socks is \(4\), and the total number of socks is \(14\). So the probability \(P_1=\frac{4}{14}=\frac{2}{7}\).

Step3: Calculate probability of second - pick

After picking a white sock for the left - foot, there are \(13\) socks left. The number of brown socks is \(4\). So the probability of picking a brown sock for the right - foot is \(P_2 = \frac{4}{13}\).

Step4: Calculate combined probability

Since these are independent events (the first pick does not affect the nature of the second pick in terms of the general principle of probability of non - replacement events), the probability of picking a white sock for the left - foot and a brown sock for the right - foot is \(P = P_1\times P_2=\frac{2}{7}\times\frac{4}{13}=\frac{8}{91}\).

Answer:

\(\frac{8}{91}\)