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    Hey there
    I am having trouble with the following question, can you help me please, Thanks

    Suppose a medical test for a certain disease has a probability of 0.99 of giving a positive result (disease is present) when applied to someone who has the disease, and a probability of 0.001 of a (false)
    positive result when applied to someone without the disease. If the disease is applied to a random
    member of the public, what is the probability of:
    • a false negative (test is negative but they do have the disease)
    When 1 in 100 people have the disease;
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    It may help to draw a tree diagram: first someone either has the disease or doesn't have it, then they take the test and get a positive or negative result.

    To calculate your probability, first notice that if someone has the disease then there's a 0.99 chance of getting a positive result. So you can therefore work out P(negative result|have disease).

    We are told that 1/100 people have the disease and we're dealing with a random member of the public. So the probability that they have the disease is P(have disease)=1/100.

    Now we can use the formula P(negative result AND have disease)= P(negative result|have disease) * P(have disease). This formula can be derived from the definition of conditional probability if you're not sure how I got it.
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    Thank you
 
 
 
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