It is given that a pair of 6-sided dice are rolled to determine who cleans the dishes.
If the sum is 5 or 6, then Rebecca cleans and if the sum is 8 or 9, Blake cleans.
If the sum is anything else they'll roll again.
It is required to determine if the process is a fair way of deciding who cleans.
The process will be fair if they both have an equal probability of cleaning.
Hence, calculate their respective probability.
Recall that the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.
The possible sums when a pair of 6-sided dice are rolled are:
The total number of possible outcomes is 6²=36.
(i) The possible outcomes for sums of a 5 or 6 are:
The number of favorable outcomes is 9.
Therefore, the probability is:
(ii) The possible outcomes for sums of 8 or 9 are:
The number of favorable outcomes is therefore 9.
The probability of a sum of 8 or 9 is:
Since they have equal probabilities, it follows that the process is fair.
Option C is the correct choice.