A red morning sky, will it rain today?

Question

In your region it rains on 30\% of days and stays dry on 70\%. A red morning sky appears on 70\% of rainy days but also on 20\% of dry days. This morning the sky is red. What is the probability it will rain today?

Accepted Answer

Imagine 100 mornings: 30 rainy and 70 dry. Count the red skies. - Rainy with red sky: 30 	imes 0.70 = 21. - Dry with red sky: 70 	imes 0.20 = 14. Of the 21 + 14 = 35 red-sky mornings, 21 turn out rainy: P(	ext{rain} \mid 	ext{red sky}) = \frac{21}{35} = \frac{3}{5} = 0.6. The red sky is real evidence for rain, lifting your belief from the 30\% base rate to 60\%, but dry days still contribute a sizable share of red skies. Takeaway. A sign that is more common under one outcome updates your belief toward it, but the everyday base rate still tempers how far the update goes.

A red morning sky, will it rain today?

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