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What that person told you is a rule of thumb, but let’s check the math carefully.

The setup

You want to estimate the probability of success $p$ in a Bernoulli/binomial process. You run $n$ trials and observe $k$ successes. Here, they are saying:

$n = 300$
$k = 300$ (all successes)
You want to be 95% confident that the true success probability $p$ is at least 99%.

Using the Clopper–Pearson (exact) interval

For binomial confidence intervals, when $k = n$ , the lower bound of the 95% confidence interval is given by:

\text{Lower bound} = (1 - \alpha)^{1/n}

where $\alpha = 0.05$ for 95% confidence.

So with $n = 300$ :

\text{Lower bound} = (0.05)^{1/300}

Numerically:

(0.05)^{1/300} \approx 0.9901

So the 95% confidence interval is about:

0.9901, , 1.0

Interpretation

With 300 successes in 300 trials, you can say with 95% confidence that the true success rate is at least ~99.01%.
This matches the claim: 300 all-successes is just enough to cross the “99% at 95% confidence” threshold.

✅ The statement is basically correct.
If you had fewer trials (say 200), the lower bound would fall below 0.99. If you had more, the bound would be tighter.

Do you want me to also show you a general formula or Python snippet you can use to compute the minimum $n$ required for arbitrary thresholds (like 99.9% at 99% confidence)?

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Binomial confidence interval

The setup

Using the Clopper–Pearson (exact) interval

Interpretation

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