When two spiral galaxies collide, the stars generally do not run into each other, but the gas clouds do collide, triggering a burst of new star formation. a. Estimate the probability that our Sun would collide with another star in the Andromeda Galaxy if a collision between the Milky Way and the Andromeda Galaxy were happening at the present time. To simplify the problem, assume that each galaxy has 100 billion stars exactly like the Sun spread evenly over a circular disk with a radius of 100,000 light-years. (Hint: First calculate the total area of 100 billion circles with the radius of the Sun and then compare that total area to the area of the galactic disk.) b. Estimate the probability that a gas cloud in our galaxy would collide with another gas cloud in the Andromeda Galaxy. To simplify the problem, assume that each galaxy contains 100,000 clouds of warm hydrogen gas, that each cloud has a radius of 300 light-years, and that these clouds are spread evenly over a circular disk with a radius of 100,000 light-years. (Hint: Use the same method as in part a.) c. Compare the probabilities you found in parts a and b and use them to explain what you see in Figure 21.5