Example 18 with 1,00,000 imaginary peopleउदाहरण 18, 1,00,000 काल्पनिक लोगों के साथExample 18, 1,00,000 imaginary logon ke saath

NCERT Example 18 · Class 12 Maths · Chapter 13 · interactive diagram

Parts and what they mean

• 1,00,000 people (imagined) (1,00,000 लोग (कल्पित)) — A convenient number so that every percentage becomes a whole number of people.
• Have HIV: 0.1% → 100 (HIV है: 0.1% → 100) — P(E) = 0.001, the prior probability.
• Do not have HIV: 99.9% → 99,900 (HIV नहीं: 99.9% → 99,900) — P(E') = 0.999.
• True positives: 90 (सही पॉज़िटिव: 90) — 90% of the 100 test positive: P(A|E) = 0.9.
• Missed cases: 10 (छूटे मामले: 10) — 10% of people with HIV test negative.
• False positives: 999 (गलत पॉज़िटिव: 999) — 1% of 99,900 healthy people test positive: P(A|E') = 0.01. This big group is why the answer is small.
• True negatives: 98,901 (सही नेगेटिव: 98,901) — 99% of 99,900 healthy people test negative.
• Bayes by counting (गिनकर बेज़) — Of the 1089 positive reports, only 90 have HIV: P(E|A) = \dfrac{90}{1089} \approx 0.083 — the same as the formula.

Original diagram drawn by Simple Learning Hub, based on NCERT Example 18. Report a mistake