A random experiment has a sample space {m,t,b,x,z,r}{m,t,b,x,z,r}. The probability of each outcomes are given as {0.1,0.05+3a,0.1+a,0.2,0.3,0.05}{0.1,0.05+3a,0.1+a,0.2,0.3,0.05}. The following events are established for this experiment: A={m,t,b}A={m,t,b}, B={t,x,z}B={t,x,z}, C={z,r}C={z,r} and D={m,b,r}D={m,b,r}.  i). Determine the value of aa. ii). Enumerate the outcomes for (A∪B)∩(C∪D)(A∪B)∩(C∪D) and find its probability. iii). Enumerate the outcomes for (A∪C)∩(B∪D)(A∪C)∩(B∪D) and find its probability.

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