Question

Researchers have discovered a new genetic marker for a form of cancer. Twelve percent of the overall population carry this marker, and of all the people who develop this cancer, 29% carry the marker. Suppose that the total frequency of cancer incidents in the population is 3%. What is the probability that a person with the marker develops cancer?

Answer 1

Answer:

The probability that a person with the marker develops cancer is 0.0725.

Step-by-step explanation:

Let's denote the events as follows:

A = a person has cancer

B = a person carries the marker.

Given:

P (A) = 0.03

P (B) = 0.12

P (B|A) = 0.29

The conditional probability of an event X provided that another event Y has already occurred is:

$P(X|Y)=\frac{P(Y|X)P(X)}{P(Y)}$

Use the conditional probability formula to compute the probability that a person with the marker develops cancer.

$P(A|B)=\frac{P(B|A)P(A)}{P(B)} =\frac{0.29\times0.03}{0.12}=0.0725$

Thus, the probability that a person with the marker develops cancer is 0.0725.