What we have here is a problem of proportions. We're assuming that the probabilities - the ratio of rainy days to total days - are equal; 3 is to 20 as something (let's call it r for "rainy days") is to 365. Mathematically, that gives us this equality:
[tex] \frac{3}{20}= \frac{r}{365} [/tex]
To solve for r, we can simply multiply either side of the equation by 365:
[tex](365) \frac{3}{20} = \frac{r}{365}(365)\\\\ \frac{365\cdot3}{20}=r [/tex]
365 and 20 have the factor 5 in common, so we can use that to reduce the fraction to:
[tex]r= \frac{73\cdot3}{4}= \frac{219}{4} = 54 \frac{3}{4} [/tex]
So, the number of rainy days, if that pattern continued, would be around 54 3/4 days, or 55, rounded up to the nearest day.
