From the diagram, we count 5 outcomes that make a sum of six.
b Let's mark all combinations that result in a sum of seven.
From the diagram, we count 6 outcomes that make a sum of seven.
c The only outcomes that are important are the ones that makes the player win or lose. Any other outcome results in a do-over, so those results might as well not count at all.
Therefore, we have 5+6=11 important outcomes.
d From Part C we know that the only important outcomes are the ones where you win or lose. Any other outcome results in a do-over. This means the number of outcomes are 11. Each time the player rolls, he has 5 outcomes of six. With this information we can calculate the probability of rolling a six before rolling a seven.
