Tom drink drives two days a week, the chance of him being caught per day is 1 in 100. What is the chance he will not be driving after a) one week? b) one year?

a) In one week he will drive drive twice, each day the probability of getting caught is 1/100 and not getting caught is 99/100. using a probability tree diagram, we can see there is only one possible outcome where he doesn't get caught on both days - (99/100 X 99/100).Therefore probability he will not be driving aka he gets caught = 1 - (99/100 X 99/100)b) In one year we can use the same logic, although in one year he will drink on 102 days (52 weeks X 2). The only way he will still be driving is if he doesn't get caught every day = (99/100)^102Therefore probability he will not be driving = 1- (99/100)^102