# What is meant by this notation for ensemble classifier error rate

The below is a picture which denotes the error of an ensemble classifier. Can someone help me understand the notation

What does it mean to have (25 and i) in brackets and what is ε^1 is it error of first classifier or the error rate raised to power i. Can someone explain this formulae.

• ${25 \choose i}$ is a binomial coefficient. The whole expression is the calculation of bernoulli distribution Commented May 22, 2022 at 9:57

$$\varepsilon^i$$ is the error rate raised to the power i. So for each value i, the formula calculates the probability of i classifiers classifying a sample incorrectly, so for i=13 we have: $$e_{13\ wrong} = {25 \choose 13} \times \varepsilon^{13} \times {(1-\varepsilon)}^{12}$$ Assuming $$\varepsilon = 35\%$$, and calculating the binomial coefficient gives us: $$e_{13\ wrong} = 5,200,300 \times 0.35^{13} \times 0.65^{12} = 0.035$$ Repeat this for $$i = 14, 15, ... , 25$$, then sum all the results to get the final answer.