Understand the relationship
The reasoning behind the result
Conditional stages prevent an orientation shortcut
A correctly oriented insert is only one part of an acceptable clone. Multiplying the required-insert fraction by the acceptable-orientation fraction among insert-positive colonies gives the fraction that passes both. Multiplying by the fraction passing further checks among that retained group gives p, the final per-colony probability.
This chain uses conditional probabilities; it does not require the three criteria to be independent. In contrast, the binomial count model assumes independent colonies with the same final p. Duplicate colonies, shared contamination or batch effects can violate that assumption.
A mean count is not a success probability
E[K]=np; P(K≥1)=1−(1−p)^n
If p=0.3, screening eight colonies has expected acceptable count 2.4. The probability of finding at least one is a different quantity: 1−0.7⁸. To require two or more acceptable colonies, the calculation must also exclude the cases with only one acceptable colony.
The requested count distribution is binomial. The planner sums its upper tail rather than substituting expected count for a probability target.
The smallest qualifying integer has a useful check
For target mode, increasing the screening count cannot reduce the chance of finding the required number. A bounded integer search finds the first count meeting the entered target and reports the probability at the preceding count.
A positive target is impossible when p is zero. A target of exactly 100% has no finite solution when 0<p<1. A target that would require more than 1000 screens is reported as outside the supported search range, not as mathematically impossible.
Follow the numbers
Eight colonies with three explicit assumptions
- Assume 75% contain the required insert, 50% of those have acceptable orientation, and 80% of those pass other checks.
- Per-colony acceptance is 0.75 × 0.50 × 0.80 = 0.30.
- For eight independent colonies, P(no acceptable colony)=0.70⁸=0.05764801.
- P(at least one)=1−0.05764801=94.235199%; the expected count is 8×0.30=2.4.
The scenario has a 94.235199% chance of at least one acceptable colony under its assumptions. It does not establish the actual cloning success rate.
Quick guide
How to use this calculator
- Supply justified scenario probabilities for the sequential criteria; each later probability is conditional on the earlier criteria passing.
- Choose the number of acceptable colonies needed and either a screening count or a probability target.
- Inspect the stage ledger and count checkpoints. The minimum-count solve checks integer counts only, up to 1000.
Calculation method
Calculation and interpretation
Turn explicit conditional success assumptions into a count-based screening scenario, with every stage and limitation visible.
p = P(insert) × P(orientation | insert) × P(other checks | insert and orientation); P(K≥r)=sum from k=r to n of C(n,k)p^k(1−p)^(n−k).
Worked example
Eight colonies with three explicit assumptions
The scenario has a 94.235199% chance of at least one acceptable colony under its assumptions. It does not establish the actual cloning success rate.
p = P(insert) × P(orientation | insert) × P(other checks | insert and orientation); P(K≥r)=sum from k=r to n of C(n,k)p^k(1−p)^(n−k).
Supported inputs
Precision and limits
Entered scenario only
No cloning method, enzyme, vector, orientation probability, screening sensitivity or colony quality is inferred. This is planning arithmetic, not an experimental protocol or guarantee.
Independent repeated screens
Assumes a fixed final per-colony probability and independent colony outcomes. Supports 1–100 required positives and at most 1000 screened colonies. Extremely small tail probabilities can underflow.
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