The Positive Test Result

ProbabilityMedium+20 XP+15

The Positive Test Result

A disease affects 1 in every 1000 people. A test for it is quite good:

If you have the disease, it comes back positive 99% of the time.
If you don't have it, it still comes back positive 2% of the time (a false positive).

You take the test. It comes back positive.

What is the probability that you actually have the disease? Answer as a percentage, rounded to one decimal place.

Hints

%

Bayesian Updating Laboratory

Explore base rates, test accuracy, true vs. false positives, and posterior probability updates.

1. Prior

Prevalence (Base Rate):

Population Grid (N = 1000 | 1 square = 1 person)

Condition Present (100)

Condition Absent (900)

Prior Probability

Condition Present:100

Total Population N:1000

Prior P(Condition):10%

Bayes' Formula Bridge

P(H|E)=

P(E|H) × P(H)P(E)

Prior P(H):0.10

Likelihood P(E|H):0.90

Evidence P(E):0.180

Result:0.5000

Prevalence (Base Rate): Shows how common the condition is in the general population. Note that the Condition Present group is a small minority (10%).

The Positive Test Result