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Q: What is the probability of the dice rolling 3 consecutive even numbers? What is the probability of the dice rolling 3 consecutive even numbers? I solved $P(\text{at least one even}) = 1-P(\text{at least one odd}) = 1-(1/6)^3 = 1/6 = 16.7\%$ However, I want to find the exact probability. The probability of me rolling the odd number $7$ in $10$ rolls is: $P(\text{at least one odd}) = 1-P(\text{at least one even}) = 1-(1/6)^2 = 1/2 = 50\%$ but the probability of me rolling the odd number $6$ in $10$ rolls is: $P(\text{at least one odd}) = 1-P(\text{at least one even}) = 1-(1/6)^2 = 1/2 = 50\%$ So the probability of me rolling the even number $6$ in $10$ rolls is: $P(\text{at least one even}) = P(\text{at least one odd}) – P(\text{both even}) = 1/2 – 1/6 = 0.375$ So the probability of me rolling the even number $7$ in $10$ rolls is: $P(\text{at least one even}) = 1 – 1/6^3 – P(\text{both even}) = 1/6 = 16.7\%$ So I found that $P(\text{both even}) = 2/3$ I get the total probability of $16.7\%$ $+$ $50\%$ $+$ $50\%$ $= 85.7\%$ But then when I plugged in $16.7\%$ for the probability of me rolling the even number $6$ in $10$ rolls, I got $10.0\%$ This confuses me because I cannot understand why I am getting $16.7\%$ for the probability of me rolling the even number $6$ in $10$ rolls when I am not asked to do that in the question. Any help would be much appreciated. A: The event “roll a double” (i.e., roll an odd number in some $10$ rolls)

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