Calculate binomial probability P(X=k) and cumulative probabilities for n trials with success probability p, enabling exact and at-most-k success likelihoods.
Calculate binomial distribution probability P(X=k) and cumulative probabilities for n trials with probability p.
| Name | Required | Description | Default |
|---|---|---|---|
| k | Yes | Number of successes (0 to n). | |
| n | Yes | Number of trials (0-1000). | |
| p | Yes | Probability of success per trial (0 to 1). |
Changes observed during successful MCP inspections.
v0.1.11Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are supplied, so the description carries the full behavioral burden. It hints that cumulative probabilities are produced alongside P(X=k) but never specifies the return shape, whether both values come back in one call, precision guarantees, or the 0-1000 n bound's effect. For a tool with zero annotation coverage this is thin.
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?
One sentence, front-loaded with the primary output P(X=k) and the key inputs. Nothing is wasted, though it is mildly under-specified rather than tightly optimized.
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?
With no output schema and no annotations, the description should clarify return values but only gestures at 'cumulative probabilities'. The three-parameter surface is simple enough that this is adequate but not complete.
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 description coverage is 100% (n, k, p each documented with ranges), so the schema already handles parameter meaning. The description restates the same three quantities without adding syntax or format detail beyond the schema, matching the baseline 3.
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?
The description gives a specific verb ('Calculate'), a named resource ('binomial distribution probability'), and the exact formula P(X=k) plus cumulative probabilities, so the agent knows exactly what computation happens. It does not explicitly differentiate itself from statistical siblings like poisson_probability or normal_distribution, which keeps it just short of a 5.
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?
There is no guidance on when to pick this over rival distribution tools (poisson_probability, normal_distribution) sitting in the same sibling list. The 'n trials with probability p' phrase implies the domain but doesn't state conditions or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.