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Wednesday, May 17, 2006

Jon's MENSA Question of the Day

--posted by JRJ on 5/17/2006

You have fifty coins totaling $1.00. You drop one down an open drain while tossing the coins in your hand. What is the chance that you have lost a quarter?

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5 Comments:

Blogger Dan S. said...

1% - Two combinations possible: one using one quarter, the other using none; combining both gives one quarter in 100 coins.

I learned from the last time you had one like this to look for more than one combination. ;-)

May 18, 2006  
Blogger JRJ said...

TRY AGAIN

May 18, 2006  
Blogger Dan S. said...

[shaking fist...] Drat!

Ok, the two combinations I came up with are:
1) 1 quarter + 2 dimes + 2 nickels + 45 pennies = $1.00
2) 2 dimes + 8 nickels + 40 pennies = $1.00

Are there more?

One coin from (1) has a 2% chance of being a quarter, and one coin from (2) has no chance of being a quarter, so (I thought...) without knowing which combination he has, the overall probability would be an average of the two, or 1%.

May 18, 2006  
Blogger JRJ said...

Book says: There are two ways you can have fifty coins totalling $1.00: two dimes, forty pennies, and eight nickels; or two dimes, forty-five pennies, two nickels, and one quarter. These arrangements are equally probable, so there is a one-half chance you had a quarter to begin with. The probablility that you then dropped that quarter from all the coins in your hand is one fiftieth. There fore, the total probability that you lost a quarter is one half times one fiftieth, or one-hundredth. (15%)

May 18, 2006  
Blogger Dan S. said...

"One-hundredth" = 1%

May 18, 2006  

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