My kids hate shopping. It means that they need to be bribed whenever we pass near a store I need to check. Last week, when visiting Marshall's, I gave in when my daughter eyed a Gumball machine. There were five colors of gum balls inside: blue, red, white, green and hot pink. Ten balls of each color, mixed well. I saw her wishing for hot pink with her tight closed fists... and remembered our last week socks' puzzle. Except that now the question is, how many gum balls do we need to get in order to be absolutely positively sure that one of them is hot pink.

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## 3 comments:

You might get NO pink gum and get 40 of the other colors; unlikely, but possible. 41 guarantees one pink. But don't buy candy for kids. Tom

41 is the correct answer.

Anything less does not guarantee a hot pink gum ball. You may get 10 red, 10 white, 10 blue and 10 green. A puzzle point for Tom!

And a blue gum ball for my daughter.

Re "no candy for kids." I wish I knew how to do it. We limit the amount though. The less we allow, the more they think about candy...

Speaking of nutrition and our eating habits, there is a program tonight that promises to be interesting: Jamie Oliver's Food Revolution on ABC.

Of course the odds of needing 41 are pretty low... You'd need 40 non-pinks in a row. And as you approached the end, the odds of not getting a pink would get very small (e.g., on the 40th pick, there would be 10 pinks in there and 1 non-pink). The odds of requiring 41 picks are 1 in 10,272,278,170. (Confession: I needed Excel to calculate that one!)

The odds are almost 50/50 after just about 3 gumballs.

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