Contingency Tables and Conditional Probability: Homework and Passing a Course

A teacher categorized students by whether they regularly completed their homework $($or not$)$ and whether they passed the course $($or not$).$ The data are in the table below.

$\backslash$table$[[,$Completed HW$,$Did not Complete HW$,$Total$],[$Passed the Course,$25,8,33],[$Did not Pass the Course,$5,14,19],[$Total$,30,22,52]]$

A student from the class is randomly selected. Determine the following probabilities. Enter your results as percents rounded to two decimal places.

What is the probability a student completed the HW$?$

What is the probability a student passed the course and did not complete the HW$?$

What is the probability a student did not pass the course or completed the HW$?$

What is the probability a student passed the course given that they completed the HW$?$