mutually exclusive events, calculate: a) P(AnB) b) P(AUB) C) P(A| B) d) P(B|A) 2) Now assume that P(A) and P(B) have the same value but that A and B are independent instead of being mutually exclusive. Recalculate the probabilities listed in a-d of part 1. 3) Now assume that A and B are neither independent nor mutually exclusive, but that it is known that P(A| B)=1/4. Recalculate the probabilities listed in a-d of part 1. Interview Outcome County Completed (C) Not at Home (N) Refused (R) Applewood 100 20 Bakingwell 115 5 Crustboro 50 15 Doughton 35 50 40 4) The above table shows the outcome of 500 interviews attempted during an opinion survey of randomly selected individuals in four counties. a) What is the probability that a randomly selected interview report was actually completed? b) what is the probability that a randomly selected interview report came from Applewood County? c) What is the probability that a randomly selected interview report involved both a Doughton County respondent and a refusal to be interviewed? d) What is the probability that a randomly selected interview report involved either a Bakingwell County respondent or a completed interview? e ) Suppose a randomly selected interview report is from Crustboro County. What is the probability the person targeted wasn't at home