NEED HELP ASAP!! PLEASE

Question

A certain affects virus 0.9% of the population. A test used to detect the virus in a person is positive 86% of the time if the person has the virus (true positive) and 15% of the time if the person does not have the virus (false postive). Fill out the remainder of the following table and use it to answer the two questions below.

Infected	Not Infected	Total
Positive Test
Negative Test
Total	900	99,100	100,000

a) Find the probability that a person has the virus given that they have tested positive. Round your answer to the nearest tenth of a percent and do not include a percent sign.

P(Infected | Positive Test)= %

b) Find the probability that a person does not have the virus given that they test negative. Round your answer to the nearest tenth of a percent and do not include a percent sign.

P(Not Infected | Negative Test) = %

Answer 1

Hi Daisy,

To fill out the table we get that 86% of those that are infected test positive, and since we know 0.9% of the population is infected, and since we can see that the total number of people in this table is 100,000, that gives us 900 people infected per 100,000 people, which is given to us in the bottom row of the table. All we have to do is multiply the number of people infected by the % that would test positive to get those that test positive and are infected.

900 * 0.86 = test positive and infected

To solve for the number of people that are infected but test negative, it is just the remaining value after subtracting the value we got for those that test positive and are infected.

900 - test positive and infected = test negative and infected

To get those that are positive and infected we first need to figure out how many people out of 100,000 are not infected. Since 0.9% of people are infected, that means that 99.1% are not infected. Out of 100,000, this gives us 99,100 people that are not infected. Since we know that 15% of people that are not infected test positive, we multiply the number of people not infected by 15% to get the number of people that are not infected but test positive anyways.

99100 * .15 = test positive and not infected

To solve for those that test negative and are not infected, we just have to subtract the number of people that test positive and are not infected from the total number of people that are not infected.

99100 - test positive and not infected = test negative and not infected

The total number of people that test positive is the sum of those that are infected and test positive plus those that test positive and are not infected.

test positive and infected + test positive and not infected = total # of people that test positive

The total number of people that test negative is the sum of those that are infected that test negative plus those that are not infected and test negative.

test negative and infected + test negative and not infected = total # of people that test negative

Now that we have filled out the table, we can answer the questions.

A) To find the probability that someone has the virus given that they test positive, we just have to divide the number of people who test positive and are infected from the total number of people that test positive. This gives us the fraction of the total number of people that test positive and are infected out of the total number of people that test positive. To turn it into a %, we then have to multiply the fraction by 100%.

(test positive and infected) / (total that test positive) * 100% = % that are infected given that they test positive

B) For part b, we follow similar steps except that this time we are dividing the number of people that test negative and are not infected by the total number of people that test negative to get the % of people that are not infect given that they test negative.

(negative and not infected) / (total that test negative) * 100% = % that are not infected given that they test negative

I hope this helps!