For The Love of Calculators!
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Little Billy has a calculator with 15 buttons. He has 10 keys for 09, a key for addition, multiplication, division, and subtraction. Finally, he has an = sign. However, Mark the Meanie messed up the programming on Billy's calculator. Now, whenever Billy presses any of the number keys, it comes up with a random singledigit number. The same goes for the four operations keys (+,,x, /). So whenever Billy tries to press the + button, the calculator chooses randomly between addition, multiplication, subtraction, and division. The only key left untouched was the = sign.
Now, if Billy were to press one number key, one operation key, then another number key, then the = button, what are the chances the answer comes out to 6?
HintThink about how many ways he could possibly get 6.
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Answer
There is a 4% chance.
There are 16 possible ways to get 6.
0+6
1+5
2+4
3+3
6+0
5+1
4+2
93
82
71
60
1x6
2x3
6x1
3x2
6/1
There are 400 possible button combinations.
When Billy presses any number key, there are 10 possibilities; when he presses any operation key, there are 4 possibilities.
10(1st#)x4(Operation)x10(2nd#)=400
16 working combinations/400 possible combinations= .04 or 4%
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Comments
doodinthemood
Sep 04, 2009
 Quite a nice little puzzle, but anyone trained to think in the standard school maths puzzle solving way won't have many problems with it. 
dalfamnest
Sep 04, 2009
 I enjoyed it  quite simple with some basic probability understanding, but a good story to make it fun. 
Nicky101
Sep 05, 2009
 Fun teaser! I forgot to switch around 6*1 and 6/1 completely slipped my mind . 
Matttoy
Sep 08, 2009
 I read the thing wrong i guess cuz I completely blanked. Then again I've only been up an hour and I'm tired! 
Stack1607
Oct 18, 2009
 Great puzzle! But I didn't notice 6/1.. 
javaguru
Dec 30, 2009
 Nice clever puzzle. Very easy, but that's OK. Although I prefer the clever and diabolically difficult puzzles, clever easy puzzles are not that common. 
BriangleJJ
Jul 08, 2010
 Agreed... Messed up a little with the 6x1 and 1x6. Now does he have a ^2 function in his calculator?? 
eighsse
Jul 27, 2013
 Fun and took a little thinking 
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