Consider the Milky Way disk, which has a 50 kpc diameter and a total height of 600 pc. Suppose that the Sun orbits precisely at the mid-plane of the disk in a circular orbit. Supernovae explosions happen randomly throughout the disk at a rate of about 2 per 100 years. Consider a spherical region around the Sun with a radius of 300 pc. Ignore the Milky Way bulge and halo in this problem; assume the Milky Way disk is perfectly uniform and extends all the way through the region of the bulge. (I.e., the Milky Way is modeled *only* as a cylindrical disk--like a hockey puck-- with constant density throughout.) If a particular supernova goes off at a random location within the disk, what is the probability that it went off in the 300 pc radius spherical region near the Sun? Express your probability as a percentage (but without writing the percent sign). [Hint: there is a 100% probability that the supernova went off somewhere in the volume of the Milky Way disk; there is a 50% probability that it went off in the right half of the disk and 25% probability that it went off in any one quadrant of the disk. In a region of very, very small volume, the probability approaches zero. Use these facts to construct a geometric argument that tells you the probability. Note also that some information provided above is used in the next problem.]

Consider the Milky Way disk, which has a 50 kpc diameter and a total height of 600 pc. Suppose that the Sun orbits precisely at the mid-plane of the disk in a circular orbit. Supernovae explosions happen randomly throughout the disk at a rate of about 2 per 100 years. Consider a spherical region around the Sun with a radius of 300 pc. Ignore the Milky Way bulge and halo in this problem; assume the Milky Way disk is perfectly uniform and extends all the way through the region of the bulge. (I.e., the Milky Way is modeled only as a cylindrical disk--like a hockey puck-- with constant density throughout.) If a particular supernova goes off at a random location within the disk, what is the probability that it went off in the 300 pc radius spherical region near the Sun? Express your probability as a percentage (but without writing the percent sign). [Hint: there is a 100% probability that the supernova went off somewhere in the volume of the Milky Way disk; there is a 50% probability that it went off in the right half of the disk and 25% probability that it went off in any one quadrant of the disk. In a region of very, very small volume, the probability approaches zero. Use these facts to construct a geometric argument that tells you the probability. Note also that some information provided above is used in the next problem.]