If a number cube is rolled 4 times,

(a)find the probability that an even number is rolled all 4 times?

(b)what is the probability that the same number is rolled at least twice?

Solution:

When a number cube is rolled one time, the possible outcome is 1,2,3,4,5,6, six outcomes

(a)

The probability an even number is rolled one time = 3/6 = 1/2

So the probability that an even number is rolled all 4 times = (1/2)^4 = 1/16

(b)

The possible outcome of 4 times = 6*6*6*6 = 1296

The outcome that four numbers are different = P(6,4) = 360

So the probability that four numbers are different = 360/1296 = 5/18

The probability that the same number is rolled at least twice = 1-the probability that four numbers are different = 1- 5/18 = 13/18

So the probability that the same number is rolled at least twice = 13/18