Question

a fair die is rolled 8 times. Find: (Please give an explanation for both answers. I'm unsure how to approach the questions)

b) what is the probability the die lands on an odd number at least 2 times

c) what is the probability the die lands on a 6 at most twice

Answer 1

b) P(landing an odd number) = Number of odd numbers / Total number of faces

= 3/6

= 0.5

The die is rolled 8 times

So, this is a binomial distribution with n = 8

P(odd number), p = 0.5

and q = 1 - p = 0.5

P(X) = nCx p^xq^n-x

P(lands on an odd number at least 2 times) = P(X$\geq$ 2)

= 1 - P(X < 2)

= 1 - P(0) - P(1)

= 1 - 0.5⁸ - 8C1x0.5x0.5⁷

= 0.9648

c) P(landing on 6), p = 1/6

q = 1 - 1/6 = 5/6

n = 8

P(die lands on a 6 at most twice) = P(X $\leq$ 2)

= P(0) + P(1) + P(2)

= (5/6)⁸ + 8C1x(1/6)x(5/6)⁷ + 8C2x(1/6)²x(5/6)⁶

= 0.2326 + 0.3721 + 0.2605

= 0.8652