In a hypothetical university in a particular degree, all students have to participate in two engineering units in year 1, called ENG101 taught in semester 1 and ENG102 taught in semester 2. While ENG101 provides foundation knowledge that is useful for ENG102, it is not a prerequisite for students to pass ENG101 before they can take ENG102. Students who fail ENG101 in semester 1 are still allowed to participate in ENG102 in semester 2 (but have to repeat ENG101 in year 2). The average success rates (averaged over all students in their first year and over all cohorts of the last decade) are as follows: 71% pass ENG101 in their first attempt and 62.89% of all students pass ENG102 in their first attempt. Out of those that pass ENG101 in their first attempt, 82% also pass ENG102 in their first attempt. Let A be the event that a student passes ENG101 in their first attempt and B be the event that a student passes ENG102 in their first attempt. (a) Describe in words the meaning of P(A B). (b) Are A and B independent events? Provide a justification for your answer. (c) Describe the meaning of P(B A) and calculate its value. (d) Do you expect A and B to be disjoint events? Describe in a sentence why the provided context supports your opinion. Calculate the probability that demonstrates that A and B are disjoint or not disjoint