Bayes' Rule with a Worked Example
A weather alert catches many late deliveries but also some on-time ones.
Bayes' Rule with a Worked Example explained visually
A weather alert catches many late deliveries but also some on-time ones. English captions are optional and start off. The complete transcript follows the written lesson.
What you will learn
A weather alert catches many late deliveries but also some on-time ones.
A practical question
Suppose one thousand trips include one hundred late deliveries. A weather alert catches eighty of those late trips. It also fires on one hundred and eighty of the nine hundred on-time trips. If an alert appears today, what fraction of alerted trips are actually late?
The useful idea
Count the alerted group: eighty late plus one hundred and eighty on time makes two hundred and sixty. Eighty divided by two hundred and sixty is about thirty-one percent. The alert caught most of the late trips, but most alerts in this example still belong to on-time deliveries.
Work through the example
That is the base-rate lesson behind Bayes' rule. Sensitivity alone doesn't give the probability the dispatcher wants; we also need how common late trips are and how often alerts appear without a delay. Change the baseline and calculate again before reusing the answer on another route.
Limits and next step
Next, we'll combine multiple features using a compact probabilistic model and inspect its assumption.
Worked example
With a 10% late rate, 80% sensitivity, and 20% false alarms, positive alerts imply about 31% late risk.
Quick check: test your understanding
Try it yourself: In the situation described above, explain the method and one reason its output might be misleading.
Check the reasoning
Bayes' rule relates a hypothesis after evidence to the evidence's likelihood and the prior. A positive test is not the same as an 80% chance of lateness.
What is the main idea behind bayes' rule with a worked example?
Bayes' rule relates a hypothesis after evidence to the evidence's likelihood and the prior.
How is it used in the example?
With a 10% late rate, 80% sensitivity, and 20% false alarms, positive alerts imply about 31% late risk.
What limitation should be checked?
A positive test is not the same as an 80% chance of lateness.
Further reading
Machine Learning — Tom M. Mitchell.
Original ToolsInVision teaching examples. Editorial approach · Suggest a correction
Accessible referenceLesson 30 transcript153 words · Video transcript · Matches the published narration and captionsOpen transcript
Suppose one thousand trips include one hundred late deliveries. A weather alert catches eighty of those late trips. It also fires on one hundred and eighty of the nine hundred on-time trips. If an alert appears today, what fraction of alerted trips are actually late?
Count the alerted group: eighty late plus one hundred and eighty on time makes two hundred and sixty. Eighty divided by two hundred and sixty is about thirty-one percent. The alert caught most of the late trips, but most alerts in this example still belong to on-time deliveries.
That is the base-rate lesson behind Bayes' rule. Sensitivity alone doesn't give the probability the dispatcher wants; we also need how common late trips are and how often alerts appear without a delay. Change the baseline and calculate again before reusing the answer on another route.
Next, we'll combine multiple features using a compact probabilistic model and inspect its assumption.