Your 80 year-old uncle goes to the doctor and says he has a positive test for prostate cancer. He comes to you and says, "You are studying math and statistics. I heard there can be false positive tests." What is the chance I actually have prostate cancer, based on my positive test? Show how you would find this probability, and then explain to him what the answer means. (Remember, you are looking at the probability of a false positive, out of all of the total positive tests)

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).