Name: Tuberculosis is quite prevalent on the border area and a huge problem. You

Question

Name: Tuberculosis is quite prevalent on the border area and a huge problem. You work for a company that has developed a test for Tuberculosis (TB). The scientists are really proud of their creation and want to bring it to market. They state that if someone has TB, there is a ninety-five percent (95%) chance that the test will come up "red" (true positive). If someone does not have TB, there is only a two percent chance that the test will come up red (false positive). Finally, the chance that anyone has TB in the border area is ten percent. Once someone takes the test and it comes up red, what is the probability that they have TB? Would you recommend these high minded scientists bring this product to the market? Why or why not? (30pts) 3. Tp=15% 9x 10 2.10 Ap= 10% , 0901 a 0196

Explanation / Answer

here let probabiliy of red =P(red) and probability of having TB =P(TB)=0.10

probability of red=P(red) =P(have TB and red +does not have TB and red)

=P(TB)*P(red|TB)+P(TBc)*P(red|TBc)=0.1*0.95+(1-0.1)*0.02=0.113

therefore probability that they have TB given red appears =P(TB)*P(red|TB)/P(red)=0.1*0.95/0.113

=0.8407

as probability of a person to have TB given test result comes positve is relatively low ; the product should further optimized.

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