
Probability question
An insurance company sells exactly 3 types of insurance: fire, auto, and flood insurance. Suppose that every customer who buys flood insurance also buys fire insurance, 20% of the customers buy fire and auto insurance, 40% of customers who buy fire insurance also buy flood insurance, and 25% of customers who buy auto insurance buy fire insurance. What is the probability that a randomly chosen customer buys flood insurance?
I'm stuck on this problem.
This is what I know.
P[flood and fire]=0.2
P[floodfire]=0.4
P[fireauto]=0.25
From the above, I see that
P[fire]=0.5
From there, I'm pretty lost. I think the point about every person that buys flood insurance, also buys fire insurance is confusing me. Any help is appreciated.
I also have a given solution from the materials, but it doesn't make much sense to me. I can post it if needed, but it doesn't make much sense to me.

Re: Probability question
Sorry, I mistyped and for some reason I don't find the edit button. Very strange. I can't edit this reply, but not my original post.
P[auto and fire]=0.2
Therefore, P[auto]=0.8