A) b) what is the probability that a person without hiv will have a test come out positive? c) what is the probability that a person with hiv will have a test come out negative? d) what is the probability that a person with hiv will have a test come out positive?

a) The cell corresponding to a positive diagnosis when the person has antibodies present as well as the cell for a negative diagnosis when the person has no antibodies present are the cells representing a CORRECT diagnosis.

The cell corresponding to a negative diagnosis when you actually have antibodies present is called a FALSE NEGATIVE and is considered as a TYPE II error.

The cell corresponding to a positive diagnosis when you actually don't have antibodies present is called a FALSE POSITIVE and is considered as a TYPE I error.

For the tree diagram for the questions below, refer to the picture attached.

b) To know the probability that a person without HIV will be diagnosed positive (false positive), we just trace the tree diagram from population to "antibodies not present" to "positive". The tree diagram will give us a value of 0.00588.

ANSWER: The probability of a false positive is 0.00588 or 0.588%.

c) We do the same thing as the previous subproblem to determine the probability that a person with HIV will be diagnosed as negative. We trace the tree diagram from population to "antibodies present" to "negative". The tree diagram will give us a value of 0.003.

ANSWER: The probability of a false negative is 0.003 or 0.3%.

d) Same thing for this subproblem. We trace the tree diagram from population to "antibodies present" to "positive" to know that the value is 0.01997.

ANSWER: The probability that a person with HIV will be diagnosed as positive is 0.01997 or 1.997%.

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