Question:
We have a bag filled with colored balls: 30 are red, 65 are blue, 110 are green, 50 are yellow, and 89 are black. If we randomly choose balls from the bag, how many must we remove to insure that we remove 70 of the same color?

A: 71
B: 110
C: 141
D: 192
E: 284 <--answer

I don't understand how the answer was explained. Please let me know how I should go about answering this question. Thank you.

Eric

The key to this problem is to come up with a way to draw as many as possible without getting 70 of the same color:

* pull all 30 red
* pull all 65 blue
* pull all 50 yellow
* pull 69 green
* pull 69 black

the next ball will have to be green or black ensuring that we have 70 of either green or black

30 + 65 + 50 + 69 + 69 = 283 ... 1 more (284 ) ensures at least 70 of green or black

Veritas Help

Thank you!

I am sorry to come back to this question, and while the solution now seems nice, I wouldn't have thought of this approach during an exam.. I would have thought of probabilities approach or something... is there any other formal approach?

You get 1 out of 5 colors every time, and while it may be very slim, but there is a chance, you'll pull them all out of the same color, while there is no "70" option in the answers, am I missing something? what's wrong in my train of thought? would love to hear back...

The key is in the wording of the original question here. We need to know how many we must remove to guarantee that we guarantee removing 70 of the same color. While it is entirely possible (and likely) that we will do this more quickly, we're looking for worst-case scenario here. We want to INSURE that we get 70 of the same color - so we try to remove as many as possible without getting 70 of the same color.

Unfortunately, I'm not aware of another "formal" approach to this, but I hope the logic makes some sense to you,

Veritas Help