Find the probability of not rolling the difference of 1.
Question
Find the probability of not rolling the difference of 1.
Solution
To answer this question, we need to understand the context. Are we rolling one die, two dice, or more? And are we looking for the absolute difference (i.e., ignoring whether it's positive or negative) or not?
Assuming we're rolling two six-sided dice and looking for the absolute difference, here's how you could calculate it:
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First, determine the total number of outcomes. When rolling two dice, there are 6*6 = 36 possible outcomes.
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Next, determine the number of outcomes where the difference between the two dice is 1. This would occur if you roll (1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,5), (5,4), (5,6), (6,5). So there are 10 such outcomes.
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The probability of an event is the number of favorable outcomes divided by the total number of outcomes. So the probability of rolling a difference of 1 is 10/36 = 5/18.
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The probability of not rolling a difference of 1 is 1 minus the probability of rolling a difference of 1. So the probability of not rolling a difference of 1 is 1 - 5/18 = 13/18.
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