Question

t is known that only 1% of U.S citizens living on East Coast will be exposed to Lyme disease. There is a blood test they can detect lyme disease, unfortunately, it's not a perfect taste. 95% of those exposed lenses will test positive using this blood test. 2% of those not expose a lot of these will also test positive.what is the probability that a randomly selected US citizen living on the east coast will test positiveAnswer Choices: 0.00050.00950.01980.0293

Answer 1

We have to find what is the probability that a randomly selected citizen of the East Coast will test positive.

This includes the sum of the true positives and false positives.

The true positives are the people that test positive and have the disease.

We know that 0.95 of the exposed will test positive.

As there is only 1% of the population exposed, the probability of randomly selecting a true positive is:

`P(TP)=0.01\cdot0.95=0.0095`

Now, we have to add the probability for the false positives.

This are the people that not being exposed (99% of the population) has a positive result in the test (2% of the tests).

This probability can be calculated as:

`P(FP)=0.99\cdot0.02=0.0198`

Then, we can now calculate the probability of selecting a person with a positive result is:

`\begin{gathered} P(P)=P(TP)+P(FP) \\ P(P)=0.0095+0.0198 \\ P(P)=0.0293 \end{gathered}`

Answer: P = 0.0293