Probability of Rolling Sum > 8 w/ Dice: Calculating Probability & Avg Rolls

AI Thread Summary
The probability of rolling a sum greater than 8 with a pair of dice is 10/36. To calculate the probability of achieving this sum in two rolls, the formula (26/36)^(n-1) * (10/36) is suggested, but there is confusion regarding the interpretation of the events as independent. Participants discuss the implications of multiplying probabilities and the expectation that the likelihood of rolling a sum greater than 8 should increase with more rolls. The conversation highlights the complexity of calculating probabilities when considering multiple rolls and the distinction between the sum of rolls versus individual roll outcomes. Understanding these nuances is essential for accurately determining the average number of rolls needed to achieve a sum greater than 8.
KingNothing
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A pair of dice is being rolled. The probability for rolling a sum greater than 8 is 10/36.

Is the probability for it taking two rolls to attain a sum greater than 8 just 26/36 times 26/36?

I need to make a table of the number of rolls it takes to obtain a sum greater than 8, and the probability that it will take that many rolls. What equation do I use? Assume n is the number of rolls it takes.

EDIT: I think I figured it out as I was walking away from the comp. Is it (26/36)^(n-1) * (10/36)?

Assuming it is, how do you find the average number of rolls it takes to get that? It looks to be about 2.4. But how do I calculate that? Is it just 36/10 or 3.6?
 
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KingNothing said:
Is the probability for it taking two rolls to attain a sum greater than 8 just 26/36 times 26/36?

Umm...but the thing is...I interpret the sentence "the probability that it will take two rolls to attain a sum > 8" to mean that you actually get a sum greater than 8 on the second roll. Otherwise, it would take 3 or more rolls! So why did you multiply by 26/36 the second time?

In general, I am not sure about the strategy of multiplying the probabilities together. Wouldn't you expect the probability of obtaining a sum > 8 to increase with larger n? Yet, if you multiply the probabilities, the product only gets smaller.

Yeah, they are not independent events, because if you consider the events independent and multiply the probabilities together (using your formula)...you are calculating the chances of getting a sum less than eight exactly n-1 times, followed by a sum > 8 the nth time. So that's NOT the way to do it.

I'll have to think about it more. No doubt somebody will explain how to do it before I figure it out.
 
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when you said you roll two times... how is it differ from rolling 4 dices at the same time? ... hope this answer your question...
 
vincentchan said:
when you said you roll two times... how is it differ from rolling 4 dices at the same time? ... hope this answer your question...

It just makes it more complicated to think of rolling four dice and dealing with sums greater than 8.
 
what grade r u in?
 
Is the probability for it taking two rolls to attain a sum greater than 8 just 26/36 times 26/36?

are u saying the sum of two rolls is greater than 8, or both rolls is greater than 8?
 

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