### Brain Teasers

# For The Love of Calculators!

Probability
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 0-9, 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 single-digit 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?

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?

### Hint

Think about how many ways he could possibly get 6.### 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

9-3

8-2

7-1

6-0

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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