a) Let X and Y are events in a sample space S and suppose that P(X)=0.30,...

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a) Let X and Y are events in a sample space S and suppose that P(X)=0.30, P(X)=0.75, and P(XY)=0.4. What is P(XY)? (4 marks) b) Five 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? ii. iii. What is the probability that none of the five people becomes ill? c) A box contains 25 yellow balls and 15 white balls. Two balls are chosen at random, one after the other, without replacement? i. What is the probability that both balls are white? (2 marks) ii. What is the probability that the second ball is white but the first ball is not? (2 marks) (3 marks) ii. (3 marks) What is the probability that the second ball is yellow? (2 marks) d) A professor uses two proofreaders Ali and Hana to check a certain manuscript. Ali misses 13% of typographical errors and Hana misses 9%. 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 2000 typographical errors, what number can be expected to be missed? (2 marks) a) Let X and Y are events in a sample space S and suppose that P(X)=0.30, P(X)=0.75, and P(XY)=0.4. What is P(XY)? (4 marks) b) Five 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? ii. iii. What is the probability that none of the five people becomes ill? c) A box contains 25 yellow balls and 15 white balls. Two balls are chosen at random, one after the other, without replacement? i. What is the probability that both balls are white? (2 marks) ii. What is the probability that the second ball is white but the first ball is not? (2 marks) (3 marks) ii. (3 marks) What is the probability that the second ball is yellow? (2 marks) d) A professor uses two proofreaders Ali and Hana to check a certain manuscript. Ali misses 13% of typographical errors and Hana misses 9%. 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 2000 typographical errors, what number can be expected to be missed? (2 marks)

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