1. A die is rolled three times. Find the probability that the sum of the outcomes is

  1. greater than 9.

36 ways for a dice. One way to roll A 12 which is 6+6 , then thees 2 ways for 11 which is 5 + 6 and 6 + 5, and then there are 3 ways to get 10. Therefore

P(>9) = P(10) + P(11) + P(12)
= 3/36 + 2/36 + 1/36 = 1/6 But since we are rolling the dice 3 times

(1/6)^3
## [1] 0.00462963
  1. an odd number.

P(at least one is odd) = 1 - P(both are even). Probability that the first die is even number is 1/2, as is the probability that the second dice.

P(both are even) = P(first is even)P(second is even) = (1/2)(1/2) = 1/4. P(at least one is odd) = 1 - 1/4 = 3/4.

But since we are rolling the dice 3 times

(3/4)^3
## [1] 0.421875