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[flood|fire]=0.4

P[fire|auto]=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.