Consider the data in Table 5 once more.

a.Evaluate the correlation between the two scores and state if there seems to be any association between the two.

b.Find the probability of upgrading for each division of the sample by the Bayes' theorem.

c.Find the probability of upgrading for each division of the sample by the nave version of the Bayes' theorem.

d.Compare your results in parts b and c and explain the difference or indifference based on observed probabilities.

Please provide your work in detail and include in-text citations.