Question

data from a medical screening test for a disease are shown in the table below.

	have disease	dont have disease
positive test (+)	190	88
negative test (-)	10	9712

calculate the probability that a person has the disease given that they test positive. give your answer as a decimal rounded to the nearest hundredth.
p(have disease | +) = \square

Explanation:

Step1: Identify relevant values

We need to find \( P(\text{Have Disease} | +) \). By the definition of conditional probability, \( P(A|B)=\frac{P(A\cap B)}{P(B)} \). Here, \( A \) is "Have Disease" and \( B \) is "Positive Test (+)". So we need the number of people who have the disease and test positive (190) and the number of people who test positive (190 + 88).

Step2: Calculate total positive tests

Total positive tests = 190 (have disease and positive) + 88 (don't have disease and positive) = \( 190 + 88 = 278 \).

Step3: Apply conditional probability formula

\( P(\text{Have Disease} | +)=\frac{\text{Number with disease and positive}}{\text{Total positive}}=\frac{190}{278} \).

Step4: Compute and round

\( \frac{190}{278}\approx0.68345 \), rounded to the nearest hundredth is 0.68.

Answer:

0.68