#1
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Average Roll
Roll a die. If you roll a 6, roll again. Repeat until you don't roll a six. Your score is the sum of all rolls.
What is the average score in this game? |
#2
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Re: Average Roll
(1/6)(1+2+3+4+5) + (1/6)(6) + (1/6)(1/6)(1+2+3+4+5)+ (1/6)(1/6)(6) + (1/6)(1/6)(1/6)(1+2+3+4+5) + ...
15/6 + 1 + 15/36 + 1/6 + 15/216 15/6(1 + 1/6 + 1/36 + ... 1/6^n) + 1(1 + 1/6 + 1/36 + ... + 1/6^n) (15/6)(6/5) + (1)(6/5) 3 + 1.2 4.2 I think, someone correct me if I'm wrong. |
#3
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Re: Average Roll
[ QUOTE ]
(1/6)(1+2+3+4+5) + (1/6)(6) + (1/6)(1/6)(1+2+3+4+5)+ (1/6)(1/6)(6) + (1/6)(1/6)(1/6)(1+2+3+4+5) + ... 15/6 + 1 + 15/36 + 1/6 + 15/216 15/6(1 + 1/6 + 1/36 + ... 1/6^n) + 1(1 + 1/6 + 1/36 + ... + 1/6^n) (15/6)(6/5) + (1)(6/5) 3 + 1.2 4.2 I think, someone correct me if I'm wrong. [/ QUOTE ] Right. Or you could just note that since the probability of not rolling a 6 is 5/6, it will take an average of 6/5 rolls to not roll one, and the average score per roll is 3.5. Then 3.5 * 6/5 = 4.2. |
#4
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Re: Average Roll
[ QUOTE ]
Right. Or you could just note that since the probability of not rolling a 6 is 5/6, it will take an average of 6/5 rolls to not roll one, and the average score per roll is 3.5. Then 3.5 * 6/5 = 4.2. [/ QUOTE ] Clever. |
#5
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Re: Average Roll
i have no idea what you just did. i'm going to spend my night figuring that out.
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