Multiple choice general knowledge math & puzzles

The local weatherman says No Rain, and his record is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain, and their record is 3/4. With no other data available, what is the chance of rain?

  1. 1/4

  2. 1/3

  3. 1/5

  4. 3/5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using Bayes' theorem for conflicting predictions: local forecaster says no rain with 2/3 accuracy (so 1/3 chance of rain), federal service says rain with 3/4 accuracy. The weighted probability of rain = (3/4) / (3/4 + 2/3) = (3/4) / (17/12) = 9/17 ≈ 0.53. However, another interpretation gives 13/24 ≈ 0.54. Both round to 3/5 = 0.60 as the closest option.

AI explanation

Using Bayes' theorem with equal prior odds for rain/no rain: P(local says no-rain AND federal says rain | actual rain) = (1/3)×(3/4) = 1/4, while the same joint probability given no rain = (2/3)×(1/4) = 1/6. Normalizing these (1/4 : 1/6, i.e., 3:2) gives a 3/5 chance that it actually rains, since the more accurate federal service's prediction carries more weight in the combined estimate.

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