Question

Toss a dice 6 times in a row. what is the probability that exactly three of the tosses are even?

Answer 1

For this problem, we can use the formula for binomial distribution:

f(x) = [n!(p^x)((1-p)^n-x)]/ x!(n-x)!

where n = total number of throws
p = probability of throwing even number (3/6 or 1/2)
n = number of times we get an even number

f(x) = [6!(0.5^3)((1-0.5)^6-3)]/ 3!(6-3)!
= [720(0.125)(0.125)] / 6(6)
= [11.25] / 36
= 0.3125