# Inspect a toy probability across serial gates

Illustrative planning brief; no automatic product import.

Synthetic planning case: A toy model requires two gates to pass. Supplied probabilities are 0.9 for A and 0.8 for B. One proposal multiplies them without stating whether the events are independent.

## Decision

The joint pass probability is 0.72 only under the supplied independence assumption. Without a joint model, the two marginal probabilities alone do not identify that result.

## Owned work

- Define the joint requirement
  - Owner role: Planning owner
  - Acceptance evidence: Both gates, rather than either gate, are required in this model.
- Expose dependence assumptions
  - Owner role: Method reviewer
  - Acceptance evidence: Shared inputs or reviewers are considered before assuming independent events.
- Bound the probability claim
  - Owner role: Decision owner
  - Acceptance evidence: The note names the conditional model and does not call 72% a validated deadline forecast.

## Workflow

1. Define the joint requirement. Check: Both gates, rather than either gate, are required in this model.
2. Expose dependence assumptions. Check: Shared inputs or reviewers are considered before assuming independent events.
3. Bound the probability claim. Check: The note names the conditional model and does not call 72% a validated deadline forecast.

## Judgment

No real gate probabilities or deadline confidence have been validated. The bounds describe this two-event mathematical model only.


## Filled manual planning note

The joint pass probability is 0.72 only under the supplied independence assumption. Without a joint model, the two marginal probabilities alone do not identify that result. Under independence, P(A and B)=0.9×0.8=0.72. With these marginals, joint probability could instead lie between max(0,0.9+0.8−1)=0.7 and min(0.9,0.8)=0.8. The multiplication chooses one dependence model. No real gate probabilities or deadline confidence have been validated. The bounds describe this two-event mathematical model only.


## Workflow questions

### Can two different owners make events independent?

No. Shared work, inputs and circumstances can still connect their outcomes.

### Are the supplied probabilities measured?

No. They are invented model inputs; the example demonstrates conditional arithmetic.

## Product connection

Use the owned checks and downloaded brief to discuss this planning decision alongside your TeamBoostAI tasks. Confirm available fields, roles and account features separately. The example is manual; it does not calculate live analytics, create work or run an experiment in the product.

Confirm account availability before adopting this manual outline.

## Original worked case

Synthetic records, manual planning only. No account import or live analytics.

### Inspect the invented case records

Event | Supplied probability | Condition
--- | --- | ---
A passes | 0.9 | Marginal only
B passes | 0.8 | Marginal only
Both pass | 0.72 | If independent

### Reasoning

Under independence, P(A and B)=0.9×0.8=0.72. With these marginals, joint probability could instead lie between max(0,0.9+0.8−1)=0.7 and min(0.9,0.8)=0.8. The multiplication chooses one dependence model.

### Bounded result

The joint pass probability is 0.72 only under the supplied independence assumption. Without a joint model, the two marginal probabilities alone do not identify that result.

### Distinct decision

This distinguishes a joint requirement from marginal probability inputs and makes independence inspectable.

### Limits

No real gate probabilities or deadline confidence have been validated. The bounds describe this two-event mathematical model only.

### Definitions and method context

- Original worked-case definitions — Definitions, policy choices, records and calculations are authored for this worksheet. No external standard, statistical validation or live product measurement is claimed.