In any 15-minute interval, there is a 20% probability that you will see at least one shooting star. Assuming the arrivals of shooting stars during non-overlapping time intervals are independent. We...

Extracted text: In any 15-minute interval, there is a 20% probability that you will see at least one shooting star. Assuming the arrivals of shooting stars during non-overlapping time intervals are independent. We will find the probability that you see at least one shooting star in a period of an hour by answering the following questions. (a) It is tempting to calculate the probability using 20%+20%+20%+20% = 4× 20% = 80%, as there are four 15-minute intervals in an hour. This is wrong. Explain why the answer is flawed. If you don't have a clue, try to use the same logic to calculate the probability of seeing at least one shooting star in a period of two hours. (b) Let A;=observing no shooting star during the ith 15-minute interval, i=1, 2, 3, 4. How can you express the event of no shooting star in an hour using A;'s? Feel free to use the set operations introduced in this class. (c) Express the event of at least one shooting star using A¡'s and compute the probability of at least one shooting star in a period of an hour.