Question

When two dice are rolled, what is the probability the two numbers will have a sum of 5?

Answer 1

When two dice are rolled, then possible outcomes are

(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)

Total possible outcomes = 36

In that, we count the ordered pairs that give us sum 5

(1,4) (2,3) (3,2) and (4,1) = 4 outcomes

Probability = (number of times the event occurs)/ (total number of outcomes)

P( sum of 5) = $\frac{4}{36}$ = $\frac{1}{9}$