Question

Find the binomial probability of rolling 5 dice and getting exactly 4 even numbers. 11.6%

15.6%
21.3%
30.9%

Answer 1

The probability of getting an even number on any one die in a single roll is
`\frac12`.

For 5 dice, the probability of rolling
`x` even numbers (where
`0\le x\le5`) is


`p(x)=\dbinom5x\left(\frac12\right)^x\left(1-\frac12\right)^(5-x)`

`p(x)=\dbinom5x\left(\frac12\right)^5`


You then have


`p(4)=\dbinom54\left(\frac12\right)^5=(5!)/(2^54!(5-4)!)=\frac5{2^5}\approx0.156=15.6\%`