I have $2$ tests I'm struggling with and I'd really appreaciate if you could help.
The questions are:
$(1)$ - A city suffers every year, on average, $5$ earthquakes, $2$ large fires and a flood. What is the probability that next year there will be at least one disaster?
$(2)$ - General strikes at federal universities are relatively rare events with a strike averaging every $5$ years. What is the probability of having at least one strike next year?
Here's what I've done so far.
$Q1$ - I tried using Poisson, which gave me coefficient $8$, then did a Sum from $1$ to $8$ using Poisson probability formula but the answer I get is not even close to the right answer.
$Q2$ - I tried using Poisson as well, which gave me the coefficient $\frac{1}{5}.$ Since on average there is only $1$ strike in $5$ years I did Poisson for just $1$, since if there is $2$ strikes it will break the average strike rate. It gave me $0.163746.$
Thanks in advance!
Hints:
1) You have to find the complement of no disaster happening. Also, not specified but my guess is the events are independent of each other, so there will be three separate Poisson variables. The result should be close to 50%.
For independent events $A$ and $B,\, p(A \& B) = p(A)p(B)$. You can extend this for three events. The events you should be looking is that for a particular disaster not happening (independent of each other). Note that, without this assumption this problem is not solvable since joint probabilities are not given.
2) Same reasoning, complement of not a single event happening. What is the probability of no strikes?