Calculate the probability of a model ensemble that uses simple majority voting m

Question

Calculate the probability of a model ensemble that uses simple majority voting making an incorrect prediction in the following scenarios. (Hint: Understanding how to use the binomial distribution will be useful in answering this question.) a. The ensemble contains 11 independent models, all of which have an error rate of 0.2. b. The ensemble contains 11 independent models, all of which have an error rate of 0.49. c. The ensemble contains 21 independent models, all of which have an error rate of 0.49

Explanation / Answer

In all these scenarios, number of independent models will be the trails. Probability of not making an error is p and probability of making an error is q

a) n=11 p=0.8 and q=0.2

Probability of making an error= 1-Probability of making no errors at all= 1-C(11,11)*(0.8)^11*(0.2)^0=0.914

b) n=11 p=0.51 and q=0.49

Probability of making an error= 1-Probability of making no errors at all= 1-C(11,11)*(0.51)^11*(0.49)^0=0.99

a) n=21 p=0.51 and q=0.49

Probability of making an error= 1-Probability of making no errors at all= 1-C(21,21)*(0.51)^21*(0.49)^0=0.99

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