Answer:
Step-by-step explanation:
We have been given that a pair of dice is rolled until a sum of either 6 or 9 appears. We are asked to find the probability that a sum of 6 occurs first.
We know that there are 5 ways, when sum of 6 can occur that are: (1,5), (2,4), (3,3), (4,2), (5,1).
There are 4 ways, when sum of 9 can occur that are: (3,6), (4,5), (5,4), (6,3).
Total possible outcomes of two dice rolled at a time are 36.
Let us find the probability that sum is not 9 as:
To find the probability that a sum of 6 occurs first, we will multiply the probability of getting sum of six with probability of not getting sum of 9 as:
Therefore, the probability that sum of 6 occurs first would be 10/81.