Two astronomers in different parts of the world make measurements M1 and M2 of the number of stars N in some small region of the sky, using their telescopes. Normally, there is a small possibility e of error by up to one star in each direction. Each telescope can also (with a much smaller probability f) be badly out of focus (events F1 and F2), in which case the scientist will undercount by three or more stars (or if N is less than 3, fail to detect any stars at all).What is Pr(N=i | M1=1 and M2=3)? (Make reasonable assumptions about Pr(N) If needed.)