mathold
posted by rama on .
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?

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.