Suppose there are 25 base classifiers. Each classifier has error rates of e = 0.35. Suppose you are using averaging as ensemble technique. What will be the probabilities that ensemble of above 25 classifiers will make a wrong prediction? Note: All classifiers are independent of each other

The correct answer is $\boxed{\text{B) }0.06}$.

The probability that an ensemble of 25 classifiers will make a wrong prediction is the probability that at least one of the classifiers makes a wrong prediction. The probability that a classifier makes a wrong prediction is $e = 0.35$. The probability that at least one of the classifiers makes a wrong prediction is $1 – (1 – e)^{25} = 1 – (0.65)^{25} \approx 0.06$.

Option A is incorrect because it is the probability that all 25 classifiers make a wrong prediction. This is much less likely than the probability that at least one classifier makes a wrong prediction.

Option C is incorrect because it is the probability that 24 of the classifiers make a wrong prediction. This is also much less likely than the probability that at least one classifier makes a wrong prediction.

Option D is incorrect because it is the probability that 23 of the classifiers make a wrong prediction. This is even less likely than the probability that at least one classifier makes a wrong prediction.