A recent college graduate is planning to take the first threeactuarial certification exams over the course of the next year, thefirst one in June, second in July and third in August. If she failsany, she will not take the remaining exams. The probability shepasses the first is 0.9. Given that she passes the first exam, shehas a 0.75 chance of passing the second and given that she passesboth the first and second, she has a 0.65 chance of passing thethird. (a) What is the probability she passes all three exams? (b)Given that she did not pass all three exams, what is theprobability that she failed the second? (c) Given that she did notpass all three exams, what is the probability that she failed thethird?
