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? Enter your answer, in simplest fraction form, in the box.

Answer 1

Answer:

$\frac{2}{3}$

Step-by-step explanation:

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 = $\frac{24}{36} =\frac{2}{3}$