Question

Two fair dice are rolled. Find the following probabilities:

a) P(the sum of the dice is five)

b) P(the sum of the dice is not five)

Answer 1

a)

When Two dice are rolled , Number of possible outcomes = 6 x6=36

Outcomes :

(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

Outcomes that favor the event : sum of the dice is five

(1,4)(2,3)(3,2)(4,1)

Number of outcomes that favor the sum of the dice is five = 4

P(the sum of the dice is five)

= Number of outcomes that favor the event :sum of the dice is five / total number of outcomes = 4/36 = 1/9

P(the sum of the dice is five) = 1/9 = 0.111111

b) P(the sum of the dice is not five) = 1 - P(the sum of the dice is five) = 1 - (1/9) = 8/9 = 0.888889

P(the sum of the dice is not five) = 8/9 = 0.888889