G4. A street is lit by n street lights arranged in a row (n > 2). If one of them burns out but its neighbors are still working?, the Department of Public Works (DPW) does not do anything. However, once two consecutive lights are out of order, the DPW immediately replaces the light bulbs in all broken lights. For example: do nothing 0 0 still do nothing replace all broken lights (i) What is the chance that the DPW will have to replace k lights, if lights break independently and with equal probability? (ii) What is the average number of lights that they have to replace in each repair? Finite sums are allowed. Compute the answers for general n, k, then compute them for n = 9, k = 4 with two digits precision after the decimal point. G4. A street is lit by n street lights arranged in a row (n > 2). If one of them burns out but its neighbors are still working?, the Department of Public Works (DPW) does not do anything. However, once two consecutive lights are out of order, the DPW immediately replaces the light bulbs in all broken lights. For example: do nothing 0 0 still do nothing replace all broken lights (i) What is the chance that the DPW will have to replace k lights, if lights break independently and with equal probability? (ii) What is the average number of lights that they have to replace in each repair? Finite sums are allowed. Compute the answers for general n, k, then compute them for n = 9, k = 4 with two digits precision after the decimal point