Assume that the disk of the Milky Way has a diameter of $40 \mathrm{kpc}$ and has a surface area $R^{2}$. Likewise, each star covers an area determined by $R^{2}.$
a. If the Milky Way contains 100 billion stars each the size of the Sun, what fraction of the galaxy's disk is actually "covered" by a star?
b. The fraction found in (a) expresses the approximate chance that when a single star passes through the Milky Way's disk, it will strike a star. If another galaxy with the same number of stars passed through the Milky Way, how many stars would you estimate would undergo direct collisions?