Answer:
1/8
Step-by-step explanation:
There's two ways you can solve this.
Method 1: Let's say you grab the socks one at a time. The first sock you grab has a 6/16 probability of being red. If the sock is red, then the second sock you grab has a 5/15 probability of being red, because there's one less red sock and one less sock total. So the overall probability is:
P = 6/16 × 5/15 = 1/8
Method 2: There are ₆C₂ ways to choose 2 red socks from 6 red socks. There are ₁₆C₂ ways to choose any 2 socks from all 16 socks. So the probability that both socks you choose are red is:
P = ₆C₂ / ₁₆C₂ = 15 / 120 = 1/8
