1 Consider a bag containing balls of three different colors: red, green and blue. Event A is drawing a red ball, Event B is drawing a ball that is either red or green and Event C is drawing a ball that is not blue. The bag contains 8 red balls, 5 green balls and 7 blue balls. a) Calculate the conditional probability of Event A given the other two events. (without using Bayes' theorem) b) Check if Event A is conditionally dependent on B and C. c) Prove Bayes' theorem for events A and B. Show all steps in your calculation