Solve both questions hand written

3. Strands of copper wire from a manufacturer are analyzed for strength and conductivity. The results from 120 strands are as follows: High Strength Low Strength High Conductivity 68 15 Low Conductivity 25 12 a) If a strand is randomly chosen, what is the probability that its conductivity is high and strength is high? (5 points) b) If a strand is randomly chosen, what is the probability that its conductivity is low or strength is low? (5 points) c) Consider the event that a strand has low conductivity and the event that the strand has low strength. Are these two events mutually exclusive? (5 points) 4. Good performance (obtaining a grade of A+) in this probability class depends on your attendance (A) and completion of assignments (C). The probability that you will receive a grade of A+ are 95%, 70%, 40%, and 0%, if you attend the class and complete the assignments, if you attend but do not complete assignments, if you do not attend but complete assignments, and if you neither attend nor complete assignments, respectively. Further assume that if you attend the class, there is a 90% probability that you will complete the assignments. The probability that you will attend the class is 0.95 and the probability that you will complete the assignments is 0.90. (a) What is the probability that you will receive an A+ in this class? (10 points) (b) If a student receives an A+, what is the probability that you attend the class and completed the assignments? (10 points)