Probability of rolling a 1 before a 6 on a dicewhat is the probability that I roll a "1" on a dice before rolling a "6". I do not know how to tackle this problem. I was thinking that this is a Geometric random variable but I do not know how to solve it.

Question

Probability of rolling a 1 before a 6 on a dicewhat is the probability that I roll a &quot;1&quot; on a dice before rolling a &quot;6&quot;. I do not know how to tackle this problem. I was thinking that this is a Geometric random variable but I do not know how to solve it.

zupa1z · Accepted Answer

Step 1By symmetry, the probability is       1    2  .Remark: We could also do it the long way. We win if we roll a 1 before we roll a 6. This can happen in several ways.1. We roll a 1 immediately. The probability that happens is       1    6  .2. We roll something that is neither a 1 nor a 6, and then roll a 1. The probability that happens is       4    6    ⋅      1    6  .3. We roll something that is neither a 1 nor a 6 twice, and then a 1. The probability that happens is             (              4        6            )        2    ⋅      1    6  .Step 2Finally, sum the infinite geometric series.

What is the probability that I roll a "1" on a dice before rolling a "6". I do not know how to tackle this problem. I was thinking that this is a Geometric random variable but I do not know how to solve it.

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