Questions: Jules and Jason collaborated in a Math146 class activity and both received 25 out of a possible 30 points. Their answers were identical. The events, Jules receiving 25 points and Jason receiving 25 points are: independent dependent disjoint Both independent and dependent

Solution Steps

To determine the relationship between the events of Jules and Jason receiving 25 points, we need to consider the definitions of independent, dependent, and disjoint events. Independent events have no influence on each other, dependent events have some influence on each other, and disjoint events cannot happen at the same time. Since their answers were identical, the events are dependent.

Let \( A \) be the event that Jules receives 25 points, and \( B \) be the event that Jason receives 25 points. Given that both received the same score, we have: \[ A: \text{Jules' score} = 25 \] \[ B: \text{Jason's score} = 25 \]

To determine the relationship between events \( A \) and \( B \), we consider the definitions:

• Independent Events: \( P(A \cap B) = P(A) \cdot P(B) \)
• Dependent Events: \( P(A \cap B) \neq P(A) \cdot P(B) \)
• Disjoint Events: \( P(A \cap B) = 0 \)

Since both received identical scores, the occurrence of one event affects the other, indicating that they are dependent.

Based on the analysis, the events are dependent because the outcome of one event influences the outcome of the other.

Final Answer