>>11170284Shit. You're right! Thank you! This is making my brain hurt.
I've reworked it more rigorously here:
Let R1, and R2 be red halves of the coin on the same side, and on the other side we have R3 be the red half of the coin and B be a blue half. Then let the ordered pair (X,Y) represent a coin that has landed on the side with X showing and Y covered. So our possibilities are (R1,R2), (R2,R1), (R3,B), (B,R3). Then it is clear to see that Pr(blue|red)=1/3, and Pr(red|blue)=2/3.
I think where I fucked up was that I wasn't considering ordered pairs when looking at Pr(red and blue). What I should have done is represent it as Pr(red then blue), which means the same thing as Pr(red and blue) but takes order into account, which is important since there is a difference between the hidden side and the showing side.
Then we get Pr(red then blue)=1/4, and Pr(red then red)=1/2, which gives Pr(blue|red)=1/3, and Pr(red|red)=2/3.
Thank you again for correcting me.
