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This may be a basic question, but if there is a twenty percent chance of rain each day for 10 days, what is the probability that it will rain at least once in that 10 day interval? I don't really know for sure how to do this problem. Thank you.

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The way you are probably intended to do this is to say that the probability it doesn't rain on a particular day is $0.8$. Therefore (?) the probability it doesn't rain for $10$ days in a row is $(0.8)^{10}$. So the probability it rains at least one day is $1-(0.8)^{10}$.

This sort of strategy is fairly often useful. If we want to find the probability that an event $E$ happens, it can be much easier to calculate first the probability that $E$ doesn't happen. In this case $E$ is the event "it rains at least one day." Then $E$ doesn't happen if it rains no days.

Remark: The reasoning that led to the answer is unfortunately dubious at best, since it assumes that raining on day $1$, $2$, $3$, and so on are independent events, like tossing a fair die $10$ times in a row. That is not a physically reasonable assumption. But without some sort of assumption, we cannot solve the problem.

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