MATH: statistic/ probalitity - need help problem with #9-11 (a-d) - related ques

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MATH: statistic/ probalitity
- need help problem with #9-11 (a-d)
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9-11. In another game with two dice, you win if you roll a sum of six, lose if you roll a sum of seven. If anything else happens you ignore the result and roll again. a. How many ways are there to get a sum of six? b. How many ways are there to get a sum of seven? c. How many possible outcomes are important in this problem? d. What is the probability of getting a sum of six before a sum of seven?

Explanation / Answer

a) No of ways to get a sum of six = 5

b) No of ways to get a sum of seven = 6

c) No of possible outcomes are important = 5 + 6 = 11

d) Probability = P(first roll getting a six and second roll getting a seven) + P(first two roll getting a six and third roll getting a seven) + P( P(first three roll getting a six and fourth roll getting a seven) + .....................

              = (5/36 * 6/36) + ((5/36)^2 * 6/36) + ((5/36)^3 * 6/36) + ................

             = (5/36 * 6/36) * ((5/36)n - 1))/(1 - 5/36)

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