Michael is an avid sport gambler and is going to incorporate a new Premier League strategy, which bets on teams that outperform expectations when it rains. Under the strategy, Arsenal (a PL football club) will generate a 35% return if it rains, and only a 5% return if it does not rain (either way Arsenal is going to outperform expectations). The other team, Manchester City, will generate a 20% return if it rains, but a -10% return if it does not rain. If there is a 30% chance of rain, what is the correlation between the returns from Arsenal and Manchester City?

Please do not use excel. Write out all steps and calculations. Thank you