Question

The experimental probability that it will rain on any given day in Houston, Texas is 3 out of 20 days. About how many days can residents predict rain out of 365 days?

Answer 1

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:

$\frac{3}{20}= \frac{r}{365}$

To solve for r, we can simply multiply either side of the equation by 365:

$(365) \frac{3}{20} = \frac{r}{365}(365)\\\\ \frac{365\cdot3}{20}=r$

365 and 20 have the factor 5 in common, so we can use that to reduce the fraction to: 

$r= \frac{73\cdot3}{4}= \frac{219}{4} = 54 \frac{3}{4}$

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.

Answer 2

So, lets set up some proportions:
The ratio of rainy days to total day - 3/20
r for rainy days to 365 - r/365


3/20 = r/365
Cross multiply.
365 * 3 = 1095
20 * r= 20r

20r = 1095
Divide 20 to both sides.
You will 54.75, which rounds out to at least 55 days.

The number of rainy days, if that pattern continued, would round up to 55 days.