probability.binomial_pmf

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnly, idempotent, closed-world. The description adds real behavioral context beyond that: k≤n constraint, p as decimal string, scipy float64 computation and 10-significant-digit rounding of the returned string. It stops short of richer output detail, but with an output schema present that's acceptable.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Three tight sentences, front-loaded with the core purpose, then constraints and result format, then the alternative-tool routing. No filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given an output schema exists, return values need not be explained, yet the description still specifies precision/rounding. Constraints, input formats and sibling routing are all covered, leaving nothing an agent needs missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 0%, so the description carries the full burden and does so well: it specifies k and n as non-negative integers with k≤n, and p as a decimal string in [0,1]. All three parameters gain semantic meaning beyond the bare schema titles.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource (compute binomial PMF P(X=k; n, p)) with the exact formula, and explicitly names the sibling binomial_cdf for the cumulative case. An agent can distinguish this from binomial_cdf without opening either schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicitly says if you need 'k or fewer' probability, use binomial_cdf, naming the alternative and the condition that selects it. The when-to-use-both split is fully specified.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.