Cumulative, at-least-one and conditional probabilities of a binomial variable
A response test is carried out independently for each participant
The probability of a response in the target category on each test is \(p=\frac{1}{4}\), and the probability of a response outside the target category is \(q=\frac{3}{4}\). The process is repeated for 4 independent tests
Let \(X\) be the number of successes
The event is \(X\le 2\)
| \(x\) | \(\Pr(X=x)\) |
|---|---|
| \(0\) | \(\square\) |
| \(1\) | \(\square\) |
| \(2\) | \(\frac{27}{128}\) |
| \(3\) | \(\frac{3}{64}\) |
| \(4\) | \(\frac{1}{256}\) |