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Math Help - Probability question

  1. #1
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    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[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.
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  2. #2
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    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
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