Question

Suppose you roll a fair six-sided die 25 times. What is the probability that you roll 5 or more 6's on that die?

Answer 1

This can be solved by using the binomial distribution to find the probability of rolling 0,1, 2, 3 or 4 6's in 25 rolls. Then that value of probability is subtracted from 1 to find the probability of 5 or more 6's.

`P(zero\ sixes)=25C0*((1)/(6))^(0)*((5)/(6))^(25)=0.0105`

`P(one\ six)=25C1*(1)/(6)*((5)/(6))^(24)=0.0524`
P(2 sixes) = 0.1258
P(3 sixes) = 0.1929

`P(4\ sixes)=25C4*((1)/(6))^(4)*((5)/(6))^(21)=0.2122`
P(0, 1, 2, 3 or 4 sixes) = 0.0105 + 0.0524 + 0.1258 + 0.1929 + 0.2122 = 0.5938
P(5 or more sixes) = 1.0000 - 0.5938 = 0.4062