(c) A Machine Learning algorithm was developed to predict whether an input image contains a human face or not. It was tested on 800 independently randomly selected images and the prediction errors were recorded. An error occurs when an input image does not contain a human face and the algorithm predicts otherwise, or when an input image contains a human face and the algorithm predicts otherwise.

(i) Identify all the relevant random variables and their respective sample spaces in the scenario given above. (ii) Express the prediction error as a random event and provide a formula to calculate its probability based on the frequentists definition of probability. (iii) Out of the 800 testing images, 30% contain a human face for which 20% were predicted wrongly. On the other hand, 65% of the images that contain no human faces were predicted correctly. Now the algorithm predicts for a new unseen image that it contains a human face. What is the probability that the new unseen image indeed contains a human face?