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Math Help - Conditional probability problem

  1. #1
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    Conditional probability problem

    Diseases I and II are prevalent among people in a certain population. It is assumed
    that 10% of the population will contract disease I sometimes during their lifetime, 15% will contract disease II eventually, and 3% will contract both diseases.

    a. Find the probability that a randomly chosen person from this population will contract at least one disease in his/her lifetime.

    b. Find the conditional probability that a randomly selected person from this population will contract both diseases, given that he or she has contracted at least one disease in his/her lifetime.

    For a, I did P(I)+P(II)-P(I or II)=0.1+0.15-0.03=0.22

    I don't know how to do b, though. Any ideas?
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    Quote Originally Posted by paupsers View Post
    Diseases I and II are prevalent among people in a certain population. It is assumed that 10% of the population will contract disease I sometimes during their lifetime, 15% will contract disease II eventually, and 3% will contract both diseases.
    a. Find the probability that a randomly chosen person from this population will contract at least one disease in his/her lifetime.

    b. Find the conditional probability that a randomly selected person from this population will contract both diseases, given that he or she has contracted at least one disease in his/her lifetime.

    For a, I did P(I)+P(II)-P(I or II)=0.1+0.15-0.03=0.22
    Let's use III to mean has both I~\&~II.
    We want to find \mathcal{P}(III|I\cup II).
    What would III\cap(I\cup II)=~?
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