Math Destroyer Test 15 Question #23

[RJ Gonzalez]

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Can somebody please help me figure out question #23 on the Math destroyer practice test 15? The question says:

Eli reaches into a bag containing 4 blue marbles, 5 green marbles, and 3 white marbles. without looking inside the bag, what is the least amount of marbles Eli should draw to guarantee 3 marbles of the same color?

The solution does not explain it very well and I cant figure it out.

Please help!

 

[DAT Destroyer]

Can somebody please help me figure out question #23 on the Math destroyer practice test 15? The question says:

Eli reaches into a bag containing 4 blue marbles, 5 green marbles, and 3 white marbles. without looking inside the bag, what is the least amount of marbles Eli should draw to guarantee 3 marbles of the same color?

The solution does not explain it very well and I cant figure it out.

Please help!

The answer cannot be 3 because you have to be extremely lucky to draw 3 of the same color.

As the solution suggests look at the worst case scenario in which you draw marbles all of different color.

Let's say you drew a blue marble after that you gonna draw a marble of different color etc....
B G W G B W ( this is an example) on the 7th pick no matter what marble you pick you're guaranteed 3 of the same color.

Hope this helps

 

[RJ Gonzalez]

Oh wow I don't know why I was reading the question as if it was asking for 3 marbles one of each color so it was throwing me off! Thank you Dr. Romano and Nancy!

 

[DAT Destroyer]

Oh wow I don't know why I was reading the question as if it was asking for 3 marbles one of each color so it was throwing me off! Thank you Dr. Romano and Nancy!

Always glad to help!

 

[pgiao]

Hello, what if the first for example 4 draws were all blue marbles? How can we assume that each pick we are choosing a different marble color?