Cumulative, at-least-one and conditional probabilities of a binomial variable
A result check is performed independently for each entry
The probability of an accepted result on each entry is \(p=\frac{2}{3}\), and the probability of a rejected result is \(q=\frac{1}{3}\). The process is repeated for 4 independent entries
Let \(X\) be the number of successes
The event is \(1\le X< 3\)
| \(x\) | \(\Pr(X=x)\) |
|---|---|
| \(0\) | \(\frac{1}{81}\) |
| \(1\) | \(\square\) |
| \(2\) | \(\frac{8}{27}\) |
| \(3\) | \(\frac{32}{81}\) |
| \(4\) | \(\frac{16}{81}\) |