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Tuesday, February 21, 2006

Jon's MENSA Question of the Day

--posted by JRJ on 2/21/2006

Billy had a coin purse with fifty coins, totaling exactly $1.00. Unfortunately, while counting them, he dropped one coin behind the radiator. What is the probability that it was a penny?

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5 Comments:

Blogger Dan S. said...

80% - He started with 40 pennies, 8 nickels, and 2 dimes.

February 21, 2006  
Blogger JRJ said...

TRY AGAIN

February 21, 2006  
Blogger Dan S. said...

Hmmm...I'm stumped.

40 + 8 + 2 = 50 total coins (check)

40 x 1c = $0.40
8 x 5c = $0.40
2 x 10c = $0.20
----------------
total = $1.00 (check)

If that's the combination of coins, then the probability of the one dropped being a penny is 40/50 = 80%.

Where am I going wrong?

February 21, 2006  
Blogger JRJ said...

The probability is 85 percent. There are only two ways in which fifty coins can total $1.00. One is forty-five pennies, two nickels, two dimes, and a quarter; the other is forty pennies, eight nickels, and two dimes. So there are eighty-five chances out of one hundred that the coin was a penny. (30%)

February 22, 2006  
Blogger Dan S. said...

Ah... Good one. Thanks for the help.

February 22, 2006  

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