Surprise test on one of five class meetings; student absent twice. Assuming exactly one test is equally likely on any of the five meetings, what is the probability the student misses the test if they are absent on two meetings?

Introduction / Context:
The original wording is ambiguous. By the Recovery-First Policy, we adopt the standard model: there is exactly one surprise test during the week, and each of the five class meetings is equally likely to host it. A student is absent on two of those five meetings. We want the probability they miss the (only) test.

Given Data / Assumptions (clarified):

• Exactly one test in the week.
• The test day is uniformly random among 5 meetings.
• The student is absent on exactly 2 specific meetings.

Concept / Approach:
The event “misses the test” occurs iff the test falls on one of the 2 absent days. With a uniform choice among 5 days, the probability is favorable days / total days.

Step-by-Step Solution:
Favorable = 2 days (absences).Total = 5 days.Probability = 2 / 5.

Verification / Alternative check:
Complement: Probability of not missing the test (i.e., test on one of the 3 present days) is 3/5. Then 1 − 3/5 = 2/5, consistent.

Why Other Options Are Wrong:
4/15, 1/15, 16/125 arise from different (independent-per-day) interpretations not implied after clarification; 3/5 is the complement.

Common Pitfalls:
Mixing the “exactly one test” model with a “test happens with probability 1/5 independently each day.” We use the standard competitive-exam model of a single, uniformly placed surprise test.

Final Answer:
2/5