Question

baye's theorem certain test for cholera gives 5% false positives, and 12% false negatives. If the test gives correct results 93% of the time, what percentage of people have cholera? Note: The probability of a false positive is P(you don't have cholera | the test says you do). The probability of a false negative is P(you do have cholera | the test says you do not).

Answer 1

Answer:

The percentage of people having cholera is 89.19%.

Step-by-step explanation:

According to the Bayes' theorem the total probability of A is:

$P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})$

Let X = a person has chorea and Y = the test is positive.

Given:

$P(X^{c}|Y)=0.05\\P(X|Y^{c})=0.12\\P(Y)=0.93$

The value of $P(X|Y)$ is:

$P(X|Y)=1-P(X^{c}|Y)=1-0.05=0.95$

Compute the value of P (X) as follows:

$P(X)=P(X|Y)P(Y)+P(X|Y^{c})P(Y^{c})\\=(0.95\times0.93)+(0.12\times(1-0.93))\\=0.8835+0.0084\\=0.8919$

The percentage of people suffering form cholera is, 0.8919 × 100 = 89.19%.

Thus, the percentage of people having cholera is 89.19%.