Dice Suppose that a red die and a green die are rolled and the numbers on...

Dice Suppose that a red die and a green die are rolled and the numbers on the sides that face upward are observed. (See Example 7 of this section and Example 2 of the first section.) (a) What is the probability that the numbers add up to 9? (b) What is the probability that the sum of the numbers is less than S?

Solutions

Expert Solution

Solution:

Given: a red die and a green die are rolled and the numbers on the sides that face upward are observed.

Sample Space S is:

n = total outcomes = 36

Part a) What is the probability that the numbers add up to 9?

P( sum =9) = ...........?

outcomes of sum =9 are: { (3,6) , (4,5) , ( 5,4) , ( 6,3) }

thus m = number of outcomes of sum 9 = 4

Thus

P( sum =9) = m / n

P( sum =9) = 4 / 36

P( sum =9) = 1 / 9

P( sum =9) = 0.111111

Part b) What is the probability that the sum of the numbers is less than 5?

P( Sum is < 5) =...............?

Outcomes for sum < 5 are:

{ (1,1) , (1,2), (1,3), (2,1) , (2,2) , (3,1) }

m = 6

Thus

P( Sum is < 5) = m / n

P( Sum is < 5) = 6 / 36

P( Sum is < 5) = 1/6

P( Sum is < 5) =0.166667

orchestra answered 1 year ago

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