Are the event that a student chooses the finance option and the event that she chooses the co-op stream independent?

Question

BlackTom AI · Accepted Answer

Let’s examine what each option claims about the relationship between two events: (1) the student choosing the finance option, and (2) the student choosing the co-op stream.
Option 1: Yes, these events are independent. This would mean that the probability of a student choosing co-op is unaffected by whether she chose finance, so P(Co-op | Finance) = P(Co-op). In many real-world settings, whether a student picks finance should not change the odds of picking co-op if the two decisions are completely unrelated. However, in most academic programs, there is often some linkage between majors and experiential learning tracks like co-op. For example, certain majors may have mandatory or highly encouraged co-op sequences, or co-op slots may be more readily available to finance majors. Given such typical curricular structures, independence is unlikely, making this option questionable.
Option 2: No, these events are not independent. If the finance option is aligned with a co-op stream (for instance, a finance major that requires or strongly recommends a co-op experience), then choosing finance increases the likelihood of choosing co-op, creating a dependency between the two choices. This reflects a common pattern where curriculum design couples majors with experiential components, leading to a relationship between the two decisions rather than complete independence.
Option 3: There is insufficient information to decide. From a purely mathematical standpoint, independence requires knowledge of probabilities or joint probabilities: P(Finance ∩ Co-op), P(Finance), and P(Co-op). If those numerical values are not provided, one might argue that we cannot conclude definitively about independence. Yet in many educational contexts, there is an implicit structural link between majors and tracks like co-op, which provides a basis for expecting dependence even without exact probabilities. In exam-oriented reasoning, a reasonable inference about curriculum structure often leads to concluding dependence, rather than labeling the relationship as indeterminable.

In summary, while formal independence requires concrete probabilistic data, the presence of curricular design that links finance majors to co-op experiences makes it plausible to treat the events as dependent, supporting option 2 over the others. In contrast, option 1 would assert independence without justification, and option 3 would ignore plausible curriculum-driven relationships.

COMM_V 190 101-104 2025W1 HW09.COMM190.2025.W1

Are the event that a student chooses the finance option and the event that she chooses the co-op stream independent?

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