QUESTION 1 20 MARKS a) Let A and B are events in a sample space S and suppose that P(A)=0.25, P(B) =0.7, and P(A' U B') = 0.45. What is P(AUB)? (4 marks) b) Fow people have been exposed to Corona virus. Once exposed, a person has a 50-50 chance of actually becoming ill. i. What is the probability that exactly one of the people becomes ill? (3 marks) i. What is the probability that none of the four people becomes ill? (2 marks) i. c) A box contains 20 green balls and 25 red balls. Two balls are chosen at random, one after the other, without replacement? What is the probability that both balls are red? (2 marks) What is the probability that the second ball is red but the first ball is not? (2 marks) What is the probability that the second ball is green? (3 marks) ii 111 d) A professor uses two proofreaders Ali and Hana to check a certain manuscript. Ali misses 9% of typographical errors and Hana misses 8%. Assume that the proofreaders work independently i. What is the probability that a randomly chosen typographical error will be missed by both proofreaders? (2 marks) If the manuscript contains 1000 typographical errors, what number can be expected to be missed? (2 marks)