Question

Two distinct number cubes, one red and one blue, are rolled together. Each number cube has sides numbered 1 through 6. What is the probability that the outcome of the roll is an even sum or a sum that is a multiple of 3?

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Answer 1

Answer: 2/3
Given: Two distinct number cubes, one red and one blue, are rolled together
To find: probability that the outcome of the roll is an even sum or a sum that is a multiple of 3
Solution:
If two dices are rolled together, possible outcomes are as follows:
(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)
So, total number of outcomes = 36
In order to find probability that the outcome of the roll is an even sum or a sum that is a multiple of 3, favourable outcomes are
(1,1) (1,2)(1,3)(1,5)
(2,1)(2,2)(2,4)(2,6)
(3,1)(3,3)(3,5)(3,6)
(4,2)(4,4)(4,5)(4,6)
(5,1)(5,3)(5,4)(5,5)
(6,2)(6,3)(6,4)(6,6)
Number of favourable outcomes = 24
Probability that the outcome of the roll is an even sum or a sum that is a multiple of 3 = Number of favourable outcomes/Total Number of outcomes = 24/36 = 2/3