Worked Solutions
1. Drake equation with your own assumptions
Any internally consistent, explicitly justified set of values is acceptable; full credit requires the calculation to be shown correctly (N = R* f_p n_e f_l f_i f_c L) with the student's own stated f_l, f_i, f_c, L, and a genuine (not perfunctory) statement of which value is least confident.
| Criterion | Points |
|---|
| Correct equation setup and arithmetic with the student's own values | 12 |
| Genuine, specific justification for each of the four chosen values | 8 |
| Genuine (not perfunctory) least-confident-term statement | 5 |
2. Dominant uncertainty term
Full credit requires an accurate comparison of the student's own N to the 6.0e-05-6.0e+05 range and a correct identification that the spread is dominated by the biological terms (f_l especially, given its factor-of-10^4 assumed range in this course's own bounding calculation), not by the astronomical terms.
| Criterion | Points |
|---|
| Correct comparison to this course's bounds | 10 |
| Correct identification of the dominant (biological) term | 10 |
3. Full synthesis critique
Full credit requires a coherent 300-500 word critique that correctly explains at least two named false-positive/degeneracy concerns (mass-radius composition degeneracy, Lecture 06; abiotic-oxygen false positive, Lecture 11; growth-versus-survival distinction, Lecture 12; or the classical-HZ-is-not-sufficient caveat, Lecture 10) as applied specifically to the chosen system, not as generic statements.
| Criterion | Points |
|---|
| Coherent, well-organized critique of appropriate length | 10 |
| Correct, system-specific application of at least two named concerns | 15 |
| Scientifically honest, appropriately hedged conclusion | 5 |
4. Honest limits statement
Any well-reasoned answer is acceptable (e.g., the mass-radius composition degeneracy, the abiotic-oxygen false positive, or the unconstrained biological Drake terms); full credit requires a genuine explanation of why stating the limitation strengthens rather than weakens the scientific claim (because an unacknowledged limitation invites a valid rebuttal, while an acknowledged one shows the claim has been tested against its most likely objection).
| Criterion | Points |
|---|
| Correctly identified, course-supported limitation | 12 |
| Genuine explanation of why acknowledging it strengthens the claim | 13 |
Grading Notes
Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Verify that the student re-derives the number for this problem's specific inputs rather than quoting a lecture example without adaptation. Watch specifically for unit-conversion errors (AU/m, days/seconds, Jupiter/Earth mass-radius units), for comparative-magnitude statements given in the wrong direction, and for level-1/level-2/level-3 data-provenance conflation (e.g., presenting an illustrative Miller-Urey bar height as a precise measured yield) -- these are the most common sources of mistakes in this course.