A study of the behaviour of a large number of drug offenders after treatment for drug abuse suggests that the likelihood of conviction within a twoiyear period after treatment may depend on the offender's education. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below. Status Within Two Years After Treatment Education Convicted Egvicted Totals 10 Years or More 0.12 0.28 0.40 9 Vears or Less 0.25 0.35 0.60 Totals 0.37 0.63 1.00 Suppose a single offender is selected from the treatment program. Here are the events of interest. A:The offender has 10 or more years of education B:The offender is convicted within 2 years after completion of treatment Find the appropriate probabilities for these events. (Enter your answers for parts (a) through (9) to two decimal places. Round your answers for parts (h) and (i) to three decimal places.) (a) A [m B (c) A n 3 [d] A u a (e) A' (t) [A U 5i( (g) (A n 5)C (h) A given that B has occurred \fAn experiment can result in one or both of events A and B with the probabilities shown in this probability table. A AC B 0.31 0.46 BC 0.20 0.03 Find the following probabilities. (Round your answers to three decimal places.) (a) P(A) 2/3 X (b) P(B) 3/7 X (c) P(An B ) (d) P(A UB) e) P(A B) (f) P(B A)Suppose that there are six prospective jurors, four men (M) and two women (W), who might be impaneled to sit on the jury in a criminal case. Two jurors are randomly selected from these six to fill the two remaining jury seats. (a) List the simple events in the experiment. (HINT: There are 15 simple events if you ignore the order of selection of the two jurors. Select all that apply.) OMM OM, W1 OM, M2 OM, W2 OM M3 OM, W OM, MA OM2 W 2 OM, M2 OM, W1 OM2M3 OM3 W2 OM, MA OMW OM, M3 MAW2 OM, MA OW W2 OMAMA X (b) What is the probability that both impaneled jurors are men? (Enter your probability as a fraction.) 4/2 X