http://psychcentral.com/news/2011/09/21/cognitive-style-tends-to-predict-religious-conviction/29646.html
Participants who gave intuitive answers to all three problems [that required reflective thinking rather than intuitive] were one and a half times as likely to report they were convinced of God’s existence as those who answered all of the questions correctly.
Importantly, researchers discovered the association between thinking styles and religious beliefs were not tied to the participants’ thinking ability or IQ.
participants who wrote about a successful intuitive experience were more likely to report they were convinced of God’s existence than those who wrote about a successful reflective experience.
I think this is the source but I can't be sure:
http://www.apa.org/pubs/journals/releases/xge-ofp-shenhav.pdf
http://lesswrong.com/lw/7o4/atheism_autism_spectrum/4vbc
You could do a couple of steps forward in solving the equations but the intuitive explanation is something along the lines of: Assuming the ball costs nothing the total comes to $1. If the total is more than that then it means that both the ball and the bat have an increased price by an equal amount. So the difference from $0 of the ball is going to be half the difference between the total and $1.