Question

If a person randomly picks two different months, what is the probability that the correlation between the two months is negative?

Answer 1

First, let's establish which months are winter months, I'm on the northern hemisphere so for me that would be December, January and February, those are 3 of the 12 months, so my probability of drawing the first winter month is 3/12, drawing a second winter - given that I have to draw a different month! - month is 3/12*2/11 so 6/132 is 1/22.

However if the first month I drew was December then there are two options for the second one, January and February. Same if I drew January or February first. All in all there are six possible orders in which I could have drawn my months. Each of these orders has a probability of 1/22, so the odds of drawing two winter months, regardless of which goes first or second, are 6/22.

As for the second one, we need to define what exactly constitutes a negative correlation.... the sales of scarves and the outside temperature have a negative correlation, when temperatures go up, the sales go down.