Question

in sals sock drawer, there are 2 red, 2 blue, 2 yellow, 2 black, and 2 green socks. if he randomly picks one sock from the drawer, and then another, which fractions should sal multiply to find the probability of choosing a pair of green socks?
(1/10)(1/9)
(2/10)(2/10)
(2/10)(1/9)
(2/10)(2/9)

Explanation:

Step1: Calculate first - pick probability

The total number of socks is \(2 + 2+2 + 2+2=10\). The number of green socks is 2. The probability of picking a green sock on the first pick is \(\frac{2}{10}\).

Step2: Calculate second - pick probability

After picking one green sock on the first pick, there is 1 green sock left and a total of 9 socks left. So the probability of picking a green sock on the second pick is \(\frac{1}{9}\).

Step3: Find combined probability

To find the probability of both events (picking a green sock first and then another green sock), we multiply the probabilities of each event. So we multiply \(\frac{2}{10}\) and \(\frac{1}{9}\).

Answer:

\((\frac{2}{10})(\frac{1}{9})\) (the third option)