Scientists claim that there is a 23% chance of seeing a shooting star each night in a certain city. (Assume that all nights are independent of each other.) Let X be the number of nights it takes until you see your first shooting star. (Round all answers to 3 decimal places.) (a) What is the average (expected) value for X? (b) What is the probability that X is at most 8? (c) What is the probability that X is more than 6? (d) What is the probability that it will take you more than 12 nights to see your first shooting star, given that it has already taken you more than 6 nights to see a shooting star