Marble Box

Probability Level 1

A box contains 200 green marbles, 200 red marbles, 200 blue marbles, 200 black marbles and 200 yellow marbles. What is the fewest number of marbles I would need to draw from the box to ensure that I pulled out at least 100 marbles of the same color?

495 498 497 None of these choices 496

3 solutions

Eli Ross Staff
Oct 5, 2015

Imagine the worst case scenario: you've drawn 99 green/red/blue/black/yellow for the first $99\cdot 5 = 495$ marbles. Then, the next one is guaranteed to give you 100 of one of the five colors, so you need $496$ marbles to guarantee that you have 100 of the same color.

This technique is referred to as the Pigeonhole Principle .

A question though, The question asked the FEWEST number of marbles, so I could be very lucky and just by picking 100 marbles and all of them are the same color.

Jingyang Tan - 5 years, 8 months ago

The question asks for "the fewest number of marbles to ENSURE". While you could do it in 100 marbles if you are lucky, you need 496 to be sure that you have at least 100 of a single color.

Eli Ross Staff - 5 years, 8 months ago

Ahmed Obaiedallah
Oct 6, 2015

I need 100 of the same color .. that may happen miraculously with first 100 or 150 or 200 but when exactly we can be sure that we pulled a 100 of the same color, that will happen when we exceed the worst case scenario which is 99 of same color for all colors by only 1 marble

So the answer will be

=5×99+1=495+1=496

Abdullah Ahmed
Oct 8, 2015

5 different colours of marbles . so the lowest will be 5×99 +1 =496 .

Marble Box

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