roll two standard dice and add the numbers. what is the probability of getting a number larger than 8 for the first time on the third roll

Step-by-step explanation:

Given

Two standard dice

Required

Probability that the outcome will be greater than 8 for the first time on the third roll

First, we need to list out the sample space of both dice

Next, is to list out the sample when outcome of both dice are added together

Next, is to get the probability that an outcome will be greater than 8

Represent this with P(E)

Next, is to get the probability that an outcome will noy be greater than 8

Represent this with P(E')

Now, we can calculate the required probability;

Probability of a number greater than 8 first on the third attempt is:

Probability of outcome not greater than 8 on the first attempt * Probability of outcome not greater than 8 on the second attempt * Probability of outcome greater than 8 on the third attempt

Mathematically;

Substitute values for P(E) and P(E')