a) Workplace accidents are categorized in three groups: minor, moderate, and severe. The probability that a given accident is minor is 0.5, that is moderate is 0.4, and that is severe is 0.1. Two accidents occur independently in one month. Calculate the probability that one of the two accidents is severe. b) Suppose that the average incidence of Covid-19 in NY State is 0.125 per hundred thousand people. What is the probability that Western New York with a population of 1.6 million people has at least twice the average incidence than NY State? c) Suppose that 105 passengers hold reservations for a 100-passenger flight. The probability that a passenger shows at the gate knowing they made a reservation is 0.94 a. On average, how many passengers show up at the gate? b. Find the probability that everyone who showed up at the gate was able to take the flight. (X is the number of the people who show up at the gate knowing that they made the reservation. If X is less or equal to 100, then everyone gets to go) d) Suppose that you have been dealt a hand of 5 cards from an ordinary 52 cards deck. After that suppose that you randomly select a card from your hand and give it back to the dealer. What is the probability that your hands contain 3 aces and that the card you gave back to the dealer is NOT an ace