a) A product has four components A, B, C, and D. The finished product must have a reliability of .95. The first three components come from a supplier, and have reliabilities of working correctly of 0.99, 0.98, and 0.995 respectively. The fourth component is being designed now. What must the reliability of component D be in order to meet the product reliability condition? Calculate your result to 4 decimal places (0.xxxx).

b) General Grant must send orders to General Butler. Carrier pigeons are the medium of choice. A single pigeon has a 0.7 probability of arriving at the proper destination in a timely fashion. How many pigeons, each carrying an identical set of orders, must Grant send in order for him to have 98% confidence (reliability) that the orders reach General Butler?

Please show all equations for better understanding. Thank you.