Probability of Picking Matching Socks from a Drawer

Imagine you have a drawer filled with 18 individual socks: 6 black, 10 white, and 2 pink. You randomly select two socks from the drawer. What are the chances of picking a pair of matching socks?

Step-by-Step Analysis

Let's delve into the probability calculations using a systematic approach. We'll start with a breakdown of the scenarios and then compute the probabilities step by step.

Cases to Consider

Black Socks

There are 6 black socks in the drawer. The probability of picking the first black sock is 6 out of 18. If the first sock is black, the probability of picking the second black sock is 5 out of the remaining 17 socks.

The combined probability for this scenario is:

(frac{6}{18} times frac{5}{17} frac{30}{306} frac{15}{153})

White Socks

There are 10 white socks in the drawer. The probability of picking the first white sock is 10 out of 18. If the first sock is white, the probability of picking the second white sock is 9 out of the remaining 17 socks.

The combined probability for this scenario is:

(frac{10}{18} times frac{9}{17} frac{90}{306} frac{45}{153})

Pink Socks

There are 2 pink socks in the drawer. The probability of picking the first pink sock is 2 out of 18. If the first sock is pink, the probability of picking the second pink sock is 1 out of the remaining 17 socks.

The combined probability for this scenario is:

(frac{2}{18} times frac{1}{17} frac{2}{306} frac{1}{153})

Total Probability of Picking Matching Socks

The total probability of picking a pair of matching socks is the sum of the probabilities of each individual matching scenario:

(frac{15}{153} frac{45}{153} frac{1}{153} frac{61}{153})

Converting this to a percentage, the probability of picking a matching pair of socks is approximately 39.87%.

Non-Matching Socks

The probability of picking two non-matching socks can be calculated as:

(1 - frac{61}{153} frac{92}{153})

This equates to approximately 60.13%.

Conclusion

In conclusion, the probability of picking two matching socks from the drawer is 61/153, which is approximately 39.87%. Contrary to the partial help suggested by some, it's always better to do your own homework and learn the process. Remember, Quora is here to help with understanding and guidance, not to do your work for you.