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.
[Math] How to determine the probability of rain over an interval of days
probability
Best Answer
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.