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The probability of rain during a winter day is 0.58, the probability of rain during a spring day is 0.38, the probability of rain during a summer day is 0.25 and the probability of rain for a fall day is 0.53. Each season is 1/4 of the year. What is the probability of rain on a randomly chosen day? In this question I got a 0.435... But I'm not really sure if I used the Bayes' theorem. I know, however, that I used the general multiplication rule and the law of total probability because in order to get the probability that it rains for any given season, I have to use the multiplication rule. And then to get the total probability of rain on any given day (in all four seasons), I have to use the law of total probability. Once more, is Bayes' theorem necessary/is used here? Thanks!

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  • $\begingroup$ You don't need Bayes here. $\endgroup$ – David G. Stork Sep 21 '20 at 17:56
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It is enough to calculate the average

$$\frac{58+38+25+53}{4}=43.5\%$$

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