7 socks
Step-by-step explanation:
chatgpt
Dom has 7 red socks, so she must pull out at least 7 socks to be 100% certain she has a matching pair. However, it is possible that she could pull out 6 socks and still have a matching pair if she happens to pull out 2 red socks in the first 6 socks. Therefore, the minimum number of socks that Dom must pull out to be 100% certain she has a matching pair is 7
Michael Lamar Follow PhD in Applied Mathematics · 7y
Originally Answered: How do you solve this probability word problem?
This is a Pigeonhole principle problem. The simple but famous theorem says that if you have more pigeons than pigeonholes, some hole must be occupied by multiple pigeons.
In your problem, you have three pigeonholes (i.e. the sock colors) so you need at least four pigeons (i.e. the socks) to ensure that at least one hole has more than one pigeon (i.e. that at least one color has at least two socks).
Assume there were not any pigeonhole with at least n/k pigeons. Then every hole has < n/k pigeons, so the total number of pigeons is < (n/k) × (# holes) = (n/k) × k = n.
quora open bard bing AI tamuedu