In a town, there are 100 houses. If the probability of rain on any given day is 0.2 and each house has an umbrella if it rains, what is the probability that at least one house will have an umbrella?
The probability that at least one house will have an umbrella is 1.

Here's the reasoning:

1. We know that the probability of rain on any given day is 0.2.
2. Since each house has an umbrella if it rains, we can say that every house in the town will have an umbrella when it rains.
3. Therefore, if it rains (which has a probability of 0.2), at least one house will have an umbrella.
4. However, even if it doesn't rain (with a probability of 0.8), at least one house still has an umbrella because they all own umbrellas regardless of whether it rains or not.
5. So, no matter the weather condition, at least one house will always have an umbrella.
6. Thus, the probability that at least one house will have an umbrella is 1 (or 100%).