Question

After several years of observations, it was found that in a given locality the month of September has an average of 12 rainy days. What is more likely: out of 8 days taken at random from this month, is it raining for 3 days or 2 days?

(the answer is 3 rainy days, But how do i get there?)

Answer 1

Explanation:

the probabilty of rain on a single day is 12/30 (as September has 30 days).

now compare this to rolling a die.

the probabilty for a specific result like "6" is 1/6 (number of desired results divided by number of possible results).

and we roll the die 8 times.

what do we expect to see ? how many 6s should we get ?

well, 8×1/6 = 8/6 = 4/3

we expect on average to see 4/3 6s (more than 1, specifically 1.33333... 6s), when we roll the die 8 times.

so, now the same here.

we pick randomly 8 days.

how many rainy days do we expect to see ?

8×12/30 = 96/30 = 32/10 = 3.2 rainy days.

that is why it is more likely to have 3 rainy days than 2 (in fact, we expect on average to have even more than 3 rainy days, specifically 3.2 rainy days, in such a sample of 8 days).