Formalize the definition of conditional probability of an event A given that B has occurred. Suppose 5% of housing projects have issues with asbestos. The sensitivity of a test for asbestos is 96% and the specificity is 89%. What is the probability that a housing project has no asbestos given a negative test expressed as a percentage to the nearest percentage point? B) Illustrate with example the conditions required for the Probability mass function to be valid C) "For any two events the probability that at least one occurs is the sum of their probabilities minus their intersection." Justify the following statement with example. Analyze Wald interval's coverage using confidence intervals and investigate their frequency performance over repeated realizations of the experiment. Consider different values of p. Write the A) R code for investigating Wald interval coverage. B) Write R code to generate Estimate, standard Error, T statistic value using Coefficient table for diamond dataset, where diamond is the predictor, and price is the outcome. C) Write the Rcode to best fit the linear regression model for the dataset student. For the given output, write the interpreted output, with marks (x) as predictor and pertormance(y) as outcome