Question

Six sided die is rolled six times. What is the or probability that the die will show an even number exactly 2 times?

Please explain how to solve this

Answer 1

Each roll of the die is an independent event.
There are `5+4+3+2+1 = 15` combinations of getting two evens and four odds.

eeoooo
eoeooo
eooeoo
eoooeo
eooooe

oeeooo
oeoeoo
oeooeo
oeoooe

ooeeoo
ooeoeo
ooeooe

oooeeo
oooeoe

ooooee

`((3/6)(3/6)(3/6)(3/6)(3/6)(3/6))^15`

`=((1/2)^(6))^(15)`

`=1/(2^90)`