(Interview) A company is interviewing candidates for a datascientist position. They estimate that the probability of a candidate being well qualied is 0.25. This is modeled by a random variable (3' that equals 1 with probability 0 25, and 1 with probability 0.75 Candidates are interviewed separately by two interviewers. The decision of the interviewers are modeled as two random variables 2'1 elq and 132 8211}, where 61 and 82 are random variables that model the probability that the interviewers make a mistake. They both equal 1 with probability 0.8 (no mistake) and 1 with probability 0.2 (mistake). (3'1, (3'2, and {1' are all mutually independent. (a) What is the probability that the outcome of both interviews is positive, i. e that 21:1 and22=1? (b) Are 2'1 and 2.2 independent? ((3) Are i1 and E2 conditionally independent given (1"