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bizboy1
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Basic Probability Question—Rolling Die!
Suppose you roll a fair six-sided die repeatedly until the first time you roll a number that you have rolled before. A) for each r=1,2,... calculate the probability pr that you roll exactly r times.
p8=p9=...=pinfinity=0
p1=0
p2=1/6
p3=5/18
I think I'm doing this the long way and the wrong way. I know these answers are right because they make sense. But it's getting to hard to count. I need insight on how I should think about this problem. It is basic probability from pitman section 1.6 problem 6. This is not homework. I am just reviewing. Please help! Thanks!
Homework Statement
Suppose you roll a fair six-sided die repeatedly until the first time you roll a number that you have rolled before. A) for each r=1,2,... calculate the probability pr that you roll exactly r times.
Homework Equations
The Attempt at a Solution
p8=p9=...=pinfinity=0
p1=0
p2=1/6
p3=5/18
I think I'm doing this the long way and the wrong way. I know these answers are right because they make sense. But it's getting to hard to count. I need insight on how I should think about this problem. It is basic probability from pitman section 1.6 problem 6. This is not homework. I am just reviewing. Please help! Thanks!