if Billy were to press one number key, one operation key, then...........what are the chances the answer comes out to 6?

Question

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?

Answer 1

4%

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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 -- 1*6 -- 2*3 -- 6*1 -- 3*2 -- 6/1
There are 10*4*10=400 possible button combinations with 10 number and 4 operation keys
16 /400= 0.04 or 4%