# removing a marble [closed]

A bag contains 3 red, 4 white, and 5 blue marbles. Jason begins removing marbles from the bag at random, one at a time. What is the maximum number of marbles he must remove to be sure that the bag consist at least 1 marble of each color?

What is the maximum number of marbles indicating to?

## closed as off-topic by Henning Makholm, John Omielan, Lee David Chung Lin, Paul Frost, cmkJul 26 at 13:32

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• I need logic on this one. The options are: (a)1 (b)2 (c)4 (d)10 (e)12 – Sec Jul 26 at 0:17
• Welcome to MSE. You'll get a lot more help, and fewer votes to close, if you show that you have made a real effort to solve the problem yourself. What are your thoughts? What have you tried? How far did you get? Where are you stuck? This question is likely to be closed if you don't add more context. Please respond by editing the question body. Many people browsing questions will vote to close without reading the comments. – saulspatz Jul 26 at 0:27
• Well, since you have only a few options, you could just try them all out. Option (a) would mean that, if you remove 1 marble, you'd still have at least one of each color in the bag but if you remove 2 then one color might have been completely removed. Option (b) would mean that, if you remove 2 marbles, you'd still have at least one of each color in the bag but if you remove 3 then one color might have been completely removed. And so on for the other options. Think about each option and see whether it's right or not. – Andreas Blass Jul 26 at 0:28
• well i need to understand what's the maximum number of marbles is indicating to. Thanks for your concern. – Sec Jul 26 at 0:30
• #Andreas Blass thanks a lot but that's not what i needed so i mentioned the options in comment rather than in the question body. And the question want to be certain ( TO BE SURE ) that the bag consist at least 1 marble of each color – Sec Jul 26 at 0:39

This a puzzle/trick and not probability at all.

If he removes $$3$$ they might all red and he won't have $$1$$ of every color.

So the answer is $$2$$. If he removes only $$2$$ he can't run out of any color and if removes $$3$$ he might run out of red.

And that's all this question asks. Nothing more.

• #fleablood you are the man. Thanks a lot dude that's what i was looking for ( the logic ). I am very much obliged. – Sec Jul 26 at 6:07

I would slightly rephrase the question.

What is the maximum number of marbles he may remove yet still be sure that the bag consist at least 1 marble of each colour?

So consider: How many marbles must be removed to become unsure that there is still at least one marble of each colour? (Without looking at the marbles removed.) The answer you require is one less than that.

• Thank you, but can you make me clear furthermore. sorry for the inconvenience – Sec Jul 26 at 0:55