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.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: