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I have a 6 sided fair dice.

Case 1 :- I have an option of throwing it twice to get a better number in my 2nd throw if I choose so. What should be the probability and expectation of this whole event?

Case 2:- I have an option of throwing it twice and thrice to get a better number in my 2nd and 3rd throw throw if I choose so. What should be the probability and expectation of this whole event?

How should I go about this? If this has already been answered, can someone point me to the right thread?

Thanks.

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    $\begingroup$ I think that Case 2 is solved here: math.stackexchange.com/questions/179534/… $\endgroup$
    – user940
    Apr 27, 2017 at 10:54
  • $\begingroup$ Thanks, that's the 1 I needed $\endgroup$
    – Deb
    Apr 27, 2017 at 10:59

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