I want to know how I would approach the following problem:
Suppose in a city, it rains with probability $0.25$ during each day of a month. What is the approximate probability that in $10$ months or more of the next 5 years ($60$ months), it rains in the first week ($7$ days).
This seems to be a straight forward question despite the wordings. I first denote $X$ as number of months in which it rains in the first week, so I want to find $P(X \geq 10)$. It seems like $X$ is a binomial distribution with $n = 60$ and $p$ unknown, so I presume I could use normal approximation to find this approximate probability.
However, I am not sure how to find $p$, the probability that it rains in the first week (for a particular month). Is it just $1 - (0.75)^7$?