Weather Forecast: The table below indicates the accuracy of a local weather repo

Question

Weather Forecast: The table below indicates the accuracy of a local weather report with respect to rain or no rain over the past year. This table gives the results of 365 consecutive days and compares whether it rained or not to whether or not rain was predicted.

If one day is randomly selected from these 365 days, what is the probability of the following? (Round your answers to 3 significant digits*.)

(a) the prediction was correct
P(the prediction was correct) =

(b) it rained given that it was predicted to rain

P(it rained | rain was predicted) =

(c) it did not rain when it was predicted to not rain
P(no rain | no rain was predicted) =

(d) Based on these results, is this weather forecast better at predicting rain or better at predicting no rain?

The weather forecast is better at predicting rain.The weather forecast is better at predicting no rain.   

     Did it actually rain?      Yes           No Report Predicted Rain     105           12 Report Predicted No Rain     39            209

Explanation / Answer

a) P(the prediction was correct) = (105+209)/365 = 0.860

b) P(it rained | rain was predicted) = 105/(105+12)= 0.897

c) P(no rain | no rain was predicted) = 209/(209+39) = 0.843

d) It is Better at predicting rain

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