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    Question:

    In a routine test for early warning of an unsuspected disease, 8% of
    those tested react (but do not all have the disease), while 7% in fact
    have the disease (but do not all react). The probability that a person
    neither has the disease nor reacts is 0.9. What is the probability that a
    person with the disease will be detected?

    I'm not too sure on how to start since I'm getting confused as to what the 8% and 7% are referring to in terms of probability. Any help is appreciated! (Probability is my worst topic in Statistics!)
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    (Original post by As_Dust_Dances_)
    Question:

    In a routine test for early warning of an unsuspected disease, 8% of
    those tested react (but do not all have the disease), while 7% in fact
    have the disease (but do not all react). The probability that a person
    neither has the disease nor reacts is 0.9. What is the probability that a
    person with the disease will be detected?

    I'm not too sure on how to start since I'm getting confused as to what the 8% and 7% are referring to in terms of probability. Any help is appreciated! (Probability is my worst topic in Statistics!)
    Using all the information we have

    P(React) = 0.08
    P(Has disease) = 0.07
    P(Not react and not have disease) = 0.9

    You are looking for the probability that a person will react given that they have the disease i.e. P(React | Has disease).

    Does this help?

    This question becomes a lot simpler if you draw a Venn diagram with a 'React' circle and a 'Diseased' circle.
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    (Original post by As_Dust_Dances_)
    Question:

    In a routine test for early warning of an unsuspected disease, 8% of
    those tested react (but do not all have the disease), while 7% in fact
    have the disease (but do not all react). The probability that a person
    neither has the disease nor reacts is 0.9. What is the probability that a
    person with the disease will be detected?

    I'm not too sure on how to start since I'm getting confused as to what the 8% and 7% are referring to in terms of probability. Any help is appreciated! (Probability is my worst topic in Statistics!)
    My teacher says that if you dislike probability then you'll dislike Statistics as a whole.

    Probability can be given as a decimal, percentage or a fraction.
    8% means 0.08. (8 out of 100).

    Start with a Venn diagram. Have two circles, one for P(react) and the other P(has the disease) . Try filling the innermost space first and work outwards leaving anything unknown. Remember intersection means "And". After you have succeeded filling all the spaces then use conditional probability to find answer.

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    For further guidance:



    P(React) = blue+purple
    P(Diseased) = pink+purple
    P(Not react and not diseased) = green
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    Thanks everyone, I just wasn't sure whether the question was asking for P(React | Has disease) or not. (+rep)
 
 
 
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