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?

Question

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.

math - Ms. Sue, Tuesday, January 29, 2013 at 10:13pm
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.
math - correction - Ms. Sue, Tuesday, January 29, 2013 at 10:20pm
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?

Answer 1

If three choices were different, and all of the next choices were the remaining purple (regardless of order), 3 + 3 = 6, so the 7th pick would be sure to match either red or blue.