Let p be the chance of rain. Raining over the weekend implies that it rains at least one day, so the chances of that happening are . Since and , then
Reading through my newly acquired statistics book, I came across the following question:
If a weather forecaster predicts 25% chance of rain for Saturday, and 25% for Sunday as well, does that mean there's a 50% chance of rain over the weekend? Yes or No and explain your answer.
My logic tells me we should take the average, which is 25%, so there should be a 25% chance of rain for the entire weekend. Am i right?
I'm not entirely sure how I feel about this answer. The math is no problem, and I would agree that .4375 would be correct if we were talking about completely independent events, like the old drawing marbles out of two bags example.
However, these are not independent in two different senses: The weather on Saturday is undeniably going to influence the weather on Sunday, and the two days flow into each other. Is there one storm front moving through, or is there a fresh one each day? Does the new one come in right at midnight?
Later on, problems will be more precise and controlled, but at the very beginning of looking into Statistics, it's important to realize that there are outside circumstances and variables infulencing these events.