Question

Your drawer contains 10 red socks and 7 blue socks. You pick 3 socks without replacement. What's the probability that at least two socks will be different colors?

Answer 1

105/136 ≈ 0.772

Explanation:

There are 3 socks and 2 colors, so they are either all the same color or 2 will be different colors.

P(different colors)

= 1 − P(same color)

= 1 − ₁₀C₃/₁₇C₃ − ₇C₃/₁₇C₃

= 1 − 120/680 − 35/680

= 1 − 155/680

= 1 − 31/136

= 105/136

≈ 0.772