Question

A six-sided die is to be rolled three times. Assume the rolls are independent and that the die is fair.

- The probability that all three rolls result in an even number is:

A) 1.0 B) 0.75 C) 0.25 D) 0.125

- The probability that at least one of the rolls is an even number is:

A) 0.125 B) 0.333 C) 0.750 D) 0.875

- The events A = exactly two of the rolls are even and B = exactly two of the rolls are odd are:

A) disjoint B) conditional C) independent D) None of the above

Answer 1

P(an even number) = 0.5

P(all three rolls result in an even number) = 0.5³

= 0.125

P(at least one of the rolls is an even number) = 1 - P(all numbers are odd)

= 1 - 0.5³

= 0.875

When exactly two dice show even, maximum 1 dies can show odd. So, A and B cannot occur at the same time

Therefore, A and B are disjoint