Question 243396: Grandma is sewing a shirt, and she needs to sew on three buttons of the same color. She has a tub with five black buttons, four brown buttons, and three white buttons. If she does not look in the tub, how many buttons must grandma pull out to guarantee that she will have at least three buttons of the same color?
A. 3 B. 4 C. 5 D. 6 E. 7
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! If she needs to be guaranteed, then the probability has to be 100%
The tub contains 5 black, 4 brown, 3 white.
Worst case possibility is she gets a different one each time.
Let a = black, b = brown, c = white
She gets:
abc abc abc
Each letter is a draw.
On the seventh draw she has to get 3 of the same color.
Let's assume she gets 2 of the same color in a row.
Each letter is a draw.
aabbcc aabbcc
On the 7th draw she has to get 2 of the same color.
I don't believe there is a worse case then that, so if she absolutely has to be guaranteed that she has 3 buttons of the same color, she would have to draw a minimnum of 7 times.
In terms of probability, the probability becomes 1 on the 7th draw.
This would be a conditional probability.
Given that she has drawn 2 black, 2 brown, and 2 white, the probability that swhe will draw the third black or brown or white on the 7th draw becomes 1.
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