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A common blood test indicates the presence of a disease 95% of the time when the disease is actually present in an individual and indicates the absence of disease 95% of the time when the disease is actually absent in an individual. The disease occurs in 1% of the population. What is the probability than an individual has the disease if their blood test is positive? Round the answer to 2 decimal places and enter it into the box below.

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Answer:0.161

Step-by-step explanation:

GIven 99% population is disease free and 95 % times it detects  correctly

1% population have disease and test detect 95% time correctly.

Probability that an individual has the disease and test show positive

[tex]P\left [ \frac{have\ disease}{test\ show\ positive}\right ][/tex]

P=[tex]\frac{0.01\times 0.95}{0.99\times 0.05+0.01\times 0.05}[/tex]

P=[tex]\frac{0.0095}{0.059}[/tex]=0.161

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