if a fair die is rolled 5 times, what is the probability of getting at most 2 fives?

Answer 1

fair die rolled 5 times, Probability of at most 2 fives = Probability of 0,1 or 2 fives

= Pr(0, 1 or 2 fives) = Pr(0 fives) + Pr(1 five) + Pr(2 fives)

1 way to get zero fives, 2 ways to get 1 five, 1 way to get 2 fives

=(5/6)^5 + 2(5/6)^4(1/6) + (1/6)^5

= 3125/7776 + 1250/7776 + 1/7776

= 4376/7776

= .5627572016 = 56.27572016 %

rounded off to nearest thousandths

=.563

or rounded off to nearest thousandths of a percent

= 56.276 %