# Rolling Dice Repeatedly(Q on Probability) Classic List Threaded 11 messages Open this post in threaded view
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## Rolling Dice Repeatedly(Q on Probability)

 This post was updated on . This question is from DEGROOT's PROBABILITY and STATISTICS. Rolling Dice Repeatedly: Suppose that two dice are to be rolled repeatedly and the sum T of the two numbers is to be observed for each roll. We shall determine the probability p that the value T=7 will be observed before the value T=8 is observed. Solution: The desired probability p could be calculated directly as follows: We could assume that the sample space S contains all sequences of outcomes that terminate as soon as either the sum T=7 or the sum T=8 is obtained. Then we could find the sum of the probabilities of all the sequences that terminate when the value T=7 is obtained. However,there is a simpler approach in this example. We can consider the simple experiment in which two dice are rolled. If we repeat the experiment until either the sum T=7 or the sum T=8 is obtained, the effect is to restrict the outcome of the experiment to one of these two values. Hence,the problem can be restated as follows: Given that the outcome of the experiment is either T=7 or T=8, determine the probability p that the outcome is actually T=7. If we let A be the event that T=7 and let B be the event that the value of T is either 7 or 8, then A∩B=A and p=Pr(A|B)=Pr(A∩B)/Pr(B)=Pr(A)/Pr(B). But Pr(A)=6/36 and Pr(B)=(6/36)+(5/36)=11/36. Hence, p=6/11. Now,my doubts are 1.) Why the author says "We could assume that the sample space S contains all sequences of outcomes that terminate as soon as either the sum T=7 or the sum T=8 is obtained. Then we could find the sum of the probabilities of all the sequences that terminate when the value T=7 is obtained." ? 2.)How can we go from lengthy sequences of outcomes that terminate as soon as either the sum T=7 or the sum T=8 is obtained to just the outcome of the experiment for which either T=7 or T=8 ? Please help.Thank you.
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## Re: Rolling Dice Repeatedly(Q on Probability)

 Please just let me know why the author stops as soon as sums 7 or 8 are obtained.(I know that stopping before getting 7 or 8 does not give any useful info for this question but why stop at all? Why can't we extend the sequences after 7 or 8 too?) PLEASE LET ME KNOW. PLEASE REPLY. THANKS.
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## Re: Rolling Dice Repeatedly(Q on Probability)

 Because when you get either 7 or 8 you get the answer to the question 'Is 7 observed before 8?'
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## Re: Rolling Dice Repeatedly(Q on Probability)

 Hi, VASUDHA, glad to see you back here. I know that that "Because when you get either 7 or 8 you get the answer to the question 'Is 7 observed before 8?'", but can't understand that why we stop ? If we go further, what will happen? (Please don't answer "NOTHING" and please elaborate the answer why nothing.) Thanks.
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## Re: Rolling Dice Repeatedly(Q on Probability)

 If u go further u will be answering the question of the nature like: "probability of getting two 7s before u get one 8" OR "probability of getting three 7s before u get one 8" OR "probability of getting two 7s before you get two 8s"... so on.. you can make this question arbitrarily difficult by making it something like: "what is the probability of getting exactly n 7s before getting m-th 8" ---  "You don't have to believe in God, but you should believe in The Book." -Paul Erdős
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## Re: Rolling Dice Repeatedly(Q on Probability)

 In reply to this post by XIPP If you continue you don't get any further information for classifying the sequence into one of the 2 categories that you are interested in-those that have 7 before 8 and those that have 8 before 7
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## Re: Rolling Dice Repeatedly(Q on Probability)

 Thank you.
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## Re: Rolling Dice Repeatedly(Q on Probability)

 In reply to this post by Sinistral Thank you, too.
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## Re: Rolling Dice Repeatedly(Q on Probability)

 do ask if it's not clear yet. or you tell why u think going beyond 7 or 8 may be important.