Can You Simplify Probability Calculations for Multiple Dice Rolls?

AI Thread Summary
To find the probability of the sum of three rolled dice being less than or equal to 9, one can avoid enumerating all 216 combinations by using probability calculations based on the outcomes of two dice and the third die. The approach involves calculating the probabilities of specific sums from two dice and then multiplying those by the probabilities of the outcomes of the third die. For instance, the probability of rolling a total of 3 with two dice can be calculated as the product of the probabilities of the individual outcomes. This method simplifies the calculation significantly, making it more efficient than listing all combinations. Understanding the probabilities of rolling two dice is crucial for this approach.
ArcanaNoir
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Homework Statement



"Find the probability of the sum of three rolled die being less than or equal to 9."

Given problems like this, my question is: is there some way to find the answer besides writing out all 216 combinations and then counting the ones that equal 9? I feel like there is, but I'm just being blind.
 
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You could consider the total as being the sum of two dice and the third. Presumably, you know the probabilities involved with rolling two dice.

For example, the probability of rolling a 3 would be P(first two=2)xP(last die=1) = (1/36)(1/6) = 1/216.
 
Ah, that looks good. Thanks!
 

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