If a fair die is rolled 5 times, what is the probability, rounded to the nearest thousandth, of getting at most 2 sixes?

Answer 1

Binomial p=1/6 N=5 k=2

Prob(X=0) = (5 choose 0) (1/6)^0 (5/6)^5

= (5/6)^5

= 0.40187757201646090534979423868313

Prob(x=1) = (5 choose 1) (1/6)^1 (5/6)^4

5 * 1/6 * (5/6)^4

= (5/6)^5 = Prob(x=0)

Prob(x=2) = (5 choose 2)(1/6)^2 (5/6)^3

= (5*4/2)(1/36)(5/6)^3

= (10/36)(5/6)^3

= (5/18)(5/6)^3

= 0.16075102880658436213991769547325

Total probability is 0.96451-