Can you solve the false positive riddle? - Alex Gendler

TL;DR

A friend offers to sell you a rock containing unobtainium, but given the possibility of false positives from an unobtainium detector, it's not a good trade.

Transcript

Mining unobtainium is hard work. The rare mineral appears in only 1% of rocks in the mine. But your friend Tricky Joe has something up his sleeve. The unobtainium detector he’s been perfecting for months is finally ready. The device never fails to detect unobtainium if any is present. Otherwise, it’s still highly reliable, returning accurate r... Read More

Key Insights

• 🥺 Trusting a high-accuracy detector without considering prior probability can lead to false positives.
• ❓ Conditional probability is crucial in determining the chances of a positive reading being valid.
• 💁 Specific information often takes precedence over general information, causing biases in decision-making.
• ❎ False positives can have negative consequences, such as unnecessary stress or wrongful arrests.
• 👋 Tricky Joe's offer is not a good deal, as the probability of the rock containing unobtainium is only 9%.
• 💄 The rarity of unobtainium makes it crucial to consider the conditional probability when using the detector.
• ☠️ The base rate fallacy arises when we neglect the base rate or prior probability in favor of immediate information.

Questions & Answers

Q: How accurate is the unobtainium detector?

The unobtainium detector is 100% accurate in detecting unobtainium, but it also has a 10% false positive rate.

Q: How many rocks in the mine contain unobtainium?

Out of 1,000 rocks in the mine, only 10 of them contain unobtainium.

Q: What is the probability that the rock Joe found contains unobtainium?

Given that 10% of the rocks without unobtainium trigger the detector, the chances of the rock Joe found containing unobtainium is 10 out of 109, which is approximately 9%.

Q: Why does this situation exemplify the base rate fallacy?

The base rate fallacy occurs when we focus on the accuracy of the detector and overlook the rarity of unobtainium. We need to consider both the detector's error rate and the overall occurrence of unobtainium.

Summary & Key Takeaways

• Tricky Joe has a device that detects unobtainium with 100% accuracy, but also has a 10% false positive rate.

• There are only 10 rocks with unobtainium out of 1,000 in the mine, making the chances of the rock Joe found containing unobtainium only 9%.

• The base rate fallacy explains why this seemed like a good deal, as our intuition focused on the accuracy of the detector, ignoring the rarity of unobtainium.