2.5 Joint Probability and Disjoint Events — Answers and Rubrics
These solutions explain the new practice tasks in this lesson. For simulation parts, a valid recorded run may differ from another learner’s run; the rubric checks the model, recorded work and interpretation.
Original generated practice for the Fall 2026 course. Return to the lesson and independent checks.
Which Locker-Code Events Are Disjoint?: worked answer
A locker-code generator selects one integer uniformly from 1 through 10. Let A={1,2,3}, B={8,9,10}, C={2,4,6,8,10}, and D={8,9,10}. A trial is one selected code; every code has positive probability 1/10.
Part a
Calculate P(A intersect B), also writing the probability with the intersection symbol. Justify whether A and B are mutually exclusive using both possible joint outcomes and joint probability.
, so . No selected code can be in both sets; the events are mutually exclusive (disjoint).
| Evidence for credit | Points |
|---|---|
| Shows no shared code and joint probability 0. | 1 |
| Uses both probability notations and explicitly justifies mutual exclusivity. | 1 |
Part b
Calculate P(C intersect D). Explain why this is a joint probability and justify whether C and D are disjoint. Distinguish the intersection set from its numerical probability.
; . The probability concerns a code satisfying both conditions. Because 8 and 10 can satisfy both, C and D are not disjoint. The set {8,10} lists outcomes; 0.20 is its probability.
| Evidence for credit | Points |
|---|---|
| Identifies {8,10} and probability .20. | 1 |
| Explains both-event occurrence and non-disjointness. | 1 |
| Distinguishes outcomes/set from probability number. | 1 |