Question

Dominic and Tony are playing a board game with a pair of six-sided dice. If Dominic can roll a total of five using the two dice, he will win the game.

a) What are all of the possible sums Dominic can roll using the pair of dice?


b) Circle the outcomes that could win the game for Dominic.


c) What is the probability that Dominic will win the game on this roll? Show your answer as a fraction and a percent.

Answer 1

(a)2,3,4,5,6,7,8,9,10,11 and 12.

(b)(1,4), (2,3), (3,2) and (4,1)

(c)
`(1)/(9)$ or 11.11\%`

Explanation:

When two six-sided dice are rolled, the 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)`

If Dominic can roll a total of five using the two dice, he will win the game.

(a) The possible sums Dominic can roll using the pair of dice is the sum

x+y where the for each outcome (x,y). These are:

`2,3,4,5,6,7\\3,4,5,6,7,8\\4,5,6,7,8,9\\5,6,7,8,9,10\\6,7,8,9,10,11\\7,8,9,10,11,12`

The possible sums are 2,3,4,5,6,7,8,9,10,11 and 12.

(b) The outcomes that could win the game for Dominic are the outcomes which adds up to 5. These are:

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

(c)Probability that Dominic will win the game on this roll

Total Possible sums =36

Number of sums that add up to 5 =4

Therefore:

The probability that Dominic will win the game on this roll

`=(4)/(36)\\=(1)/(9)\\ $Expressed as a percentage, we have$:\\(1)/(9) * 100 =11.11\%`