the data represent the results for a test for a certain disease. assume one individual from the group is…
the data represent the results for a test for a certain disease. assume one individual from the group is randomly selected. find the probability of getting someone who tested negative, given that he or she had the disease.\nthe individual actually had the disease\n| |yes|no|\n|--|--|--|--|\n|positive|126|24|\n|negative|11|139|
Answer
Explanation:
Step1: Recall conditional - probability formula
The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of this problem, let $A$ be the event of testing negative and $B$ be the event of having the disease. Then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of people who have the disease and tested negative, and $n(B)$ is the number of people who have the disease.
Step2: Identify relevant values from the table
From the table, the number of people who have the disease ($B$) is $n(B)=120 + 11=131$ (the sum of positive - test and negative - test among those with the disease). The number of people who have the disease and tested negative ($A\cap B$) is $n(A\cap B)=11$.
Step3: Calculate the probability
$P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{11}{131}\approx0.084$.
Answer:
$\frac{11}{131}$