Question

In your sock drawer, you have 4 blue socks, 5 gray socks, and 3 black socks. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability that you end up wearing

Answer 1

The probability of grabbing two matching socks randomly from a drawer containing 4 blue, 5 gray, and 3 black socks is 14/33.

Step-by-step explanation:

You have a total of 12 socks in your drawer. To find the probability of grabbing any two socks that match, you'll need to calculate the probability for each color and then add those probabilities together. The probability is calculated by dividing the number of ways to draw two matching socks by the total number of ways to draw any two socks.

Probability of drawing two blue socks:

P(2 Blue) = (4/12) * (3/11) = 1/11

Probability of drawing two gray socks:

P(2 Gray) = (5/12) * (4/11) = 5/33

Probability of drawing two black socks:

P(2 Black) = (3/12) * (2/11) = 1/22

The total probability is P(Total) = P(2 Blue) + P(2 Gray) + P(2 Black) = 1/11 + 5/33 + 1/22 = 14/33.

Hence, the probability of wearing matching socks is 14/33.