Certain virus infects one in every 300 people. a test used to detect the virus in a person is positive 80% of the time if the person has the virus and 8% of the time if the person does not have the virus. (this 8% result is called a false positive.) let a be the event "the person is infected" and b be the event "the person tests positive". hint: make a tree diagram a) find the probability that a person has the virus given that they have tested positive, i. e. find p(a|b). round your answer to the nearest tenth of a percent and do not include a percent sign. p(a|b)= % b) find the probability that a person does not have the virus given that they test negative, i. e. find p(a'|b'). round your answer to the nearest tenth of a percent and do not include a percent sign. p(a'|b') =

The probability that a person has the virus given that they have tested positive is P(A|B)=0.032.

The probability that a person does not have the virus given that they have tested negative is P(A'|B')=0.999.

Step-by-step explanation:

a) The probability of B: "the person tests positive" is the sum of:

- The probability that a person has the virus and the test is positive.

- The probability that a person don't have the virus but the test is positive.

Then, the probability of B: "the person tests positive" is

We have

Then

The probability that a person has the virus given that they have tested positive is P(A|B)=0.032.

b) The probability P(A'|B') is

We have

Then

The probability that a person does not have the virus given that they have tested negative is P(A'|B')=0.999.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

answer: it's d

step-by-step explanation: