A university is applying classification methods in order to identify alumni who may be interested in donating money. The university has a database of 58,205 alumni profiles containing numerous variables. Of these 58,205 alumni, only 576 have donated in the past. The university has oversampled the data and trained a random forest of 100 classification trees. For a cutoff value of 0.5, the following confusion matrix summarizes the performance of the random forest on a validation set:

PredictedActualDonationNo DonationDonation268 20 No Donation5,375 23,439

The following table lists some information on individual observations from the validation set:

Probability of PredictedObservation IDActual Class Donation ClassADonation 0.8 DonationBNo Donation 0.1 No DonationCNo Donation 0.6 Donation

(a)

Choose the correct explanation for how the probability of Donation was computed for the three observations.

(i)The probability of Donation for each observation is the proportion of the 100 individual classification trees that classified the observation as "Donation."(ii)The probability of Donation for each observation is the proportion of the 100 individual classification trees that classified the observation as "No Donation."(iii)The probability of Donation for each observation is the ratio of the individual classification trees that classified the observation as "Donation" and those that classified it as "No Donation."(iv)The probability of Donation for each observation is the ratio of the individual classification trees that classified the observation as "No Donation" and those that classified it as "Donation." - Select your answer -Option (i)Option (ii)Option (iii)Option (iv)Item 1

Why were Observations A and C classified as Donation and Observation B was classified as No Donation?

If required, round your answers to one decimal place.

The probability of Donation for Observation A is . It is - Select your answer -greater lessItem 3 than 0.5, so Observation A is classified as Donation by the random forest.

The probability of Donation for Observation B is . It is - Select your answer -greater lessItem 5 than 0.5, so Observation B is classified as No Donation by the random forest.

The probability of Donation for Observation C is . It is - Select your answer -greater lessItem 7 than 0.5, so Observation C is classified as Donation by the random forest.