1. Redundancy in Aircraft Radios-The FAA requires that commercial aircraft used for flying in instrument conditions must have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.0035. What is the probability that a particular flight may be safe with at least one working radio? Why does the usual rounding rule of three significant digits not work here? Is this probability high enough to ensure flight safety?
2. Illinois lottery
a. In the Illinois Little lotto game, you win the jackpot by selecting five different whole numbers from 1-39 and getting the same five numbers (in any order) that are later drawn. What is the probability of winning a jackpot in this game?
b. In the Illinois Pick 3 game, you win a bet by selecting three digits (with repetition allowed) and getting the same three digits in the exact same order as they are later drawn. What is the probability of winning this game?
c. The Illinois pick 3 game returns $500 for a winning $1 ticket. What should be the return if Illinois were to run this game for profit?