A bag got mix up 6 pairs of shoes – 2 red, 2 blue, and 2 purple. Picking randomly, how many shoes must I pick before for sure that there is one matching pair in red or blue?
Ms Sue answered 4. Request for explanation please.
With 3 picks she could have gotten 1 red, 1 blue, and 1 purple shoe. On the 4th pick, she has to pick one of the colors she already had. Therefore, it will take 4 draws before she'd be sure she had a pair.
I just read it again -- to see that you must have a matching pair in red or blue.
You'll need 5 picks instead of 4.
Sue,
there are possibilities beyond what you may have quoted...did i misunderstand here?
To determine the minimum number of shoes you must pick to ensure that there is one matching pair in red or blue, you need to consider the worst-case scenario.
Let's analyze the possibilities step by step:
1. Picking the first shoe: No matter which shoe you pick, there won't be any matching pair yet.
2. Picking the second shoe: Regardless of the color, it cannot match with the first shoe you picked.
3. Picking the third shoe: In the worst-case scenario, the third shoe will match with either the first or second shoe, resulting in a pair. However, since there are only two colors left (blue and purple), and each color has two shoes, at least one pair will be formed.
Therefore, you need to pick a minimum of three shoes to ensure that there is one matching pair in red or blue.