Back At It Again With The White Vans

Probability Level 1

Daniel has three pairs of shoes in his closet: 2 red shoes, 2 black shoes, and 2 white shoes. If Daniel selects shoes randomly from his closet, how many must he pull out to ensure he has a matching pair?

4 2 6 3

3 solutions

Daniel Liu
Feb 23, 2016

In the worst-case scenario, I pull out one of each color with my first three draws, so the answer must be greater than three.

I claim the answer is four. If I draw four shoes out of three types of shoes, by the Pigeonhole Principle there exists two shoes I drew with the same color, i.e a matching pair. Thus, four draws is the minimum possible.

$\huge \color{#D61F06}{\text{Damn Daniel!!!!!}}$

Arulx Z - 5 years, 3 months ago

Wait what if you pull 2 black shoes in a row

Aditya Guin - 5 years, 3 months ago

You need four to ENSURE that there is a matching pair. Say, you pick the shoes without looking at what you pick. You cannot be 100% sure that you have a matching pair (of any color) unless you pick four.

Luke Yoon - 5 years, 3 months ago

As Luke said, the question says to ENSURE he has a matching pair. If you think the answer is 2, then there's not a guarantee I have a match when I pull 2.

Andrew Ellinor - 5 years, 3 months ago

Dragos Ionut
Feb 24, 2016

I think the right answer should be 7, because you cand draw two left shoes of the same color, but they don't count as a pair.

Tyson Jelicich
Feb 24, 2016

At his unluckiest, he will choose 1 of each colour in sequence. in order for him to get any pair, one more shoe must be picked, therefore 3+1=4

On another note DAMN DANIEL, BACK AT IT AGAINST WITH THE WHITE VANS

Back At It Again With The White Vans

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