A teaching assistant is grading programs written by students enrolled in an entry level computer science course. The TA has been asked to look for two types of errors in student work: syntax errors, and coding errors. The probability that a student's program will contain one or more syntax error is 10%. On the other hand the probability that a student's program will contain one or more coding error is 20%. Given that a student's program has one or more syntax error(s), the probability that the program will also contain one or more coding error(s) is 50%. The grading scheme used by the TA is as follows. If a program only contains syntax errors (regardless of how many), the TA deducts 5 points. If a program only contains coding errors (regardless of how many), the TA deducts 4 points. If a program contains both syntax error(s) and coding error(s), then the TA deducts 10 points. Set up a contingency table to display probabilities as stated in the problem. Calculate the expected value for the number of points that will be deducted per student program. Are the probabilities of coding and syntax errors independent?