"Below is the account of a well-known test, and an embarrassing one for the medical profession. The following famous **quiz was given to medical doctors** (which I borrowed from the excellent [[Deborah Bennett]]’s Randomness). "A test of a disease presents a rate of **5% false positives**. The **disease strikes 1/1,000 of the population**. People are **tested at random**, regardless of whether they are suspected of having the disease. "A patient’s test is positive. **What is the probability of the patient being stricken with the disease?** "Most doctors answered 95%, simply taking into account the fact that the test has a 95% accuracy rate. **The answer is the conditional probability that the patient is sick and the test shows it**—close to 2%. Less than one in five professionals got it right. "I will simplify the answer (using the frequency approach). - Assume **no false negatives**. - Consider that **out of 1,000 patients who are administered the test, one will be expected to be afflicted** with the disease. - Out of a population **of the remaining 999 healthy patients, the test will identify about 50 with the disease** (it is 95% accurate). "The correct answer should be that **the probability of being afflicted with the disease for someone selected at random who presented a positive test is the following ratio: here 1 in 51.** --- **Tags** -- [[quotes]], [[conditional-probabilities]], [[probability-distributions]], [[fooled-by-randomness]], [[statistics]], [[data-analytics]] **Source** -- [[202410121132 - B - Fooled by Randomness]]