PSYA02 has 5,000 students. there are total of 50 questions with 4 options each. The instructor observed that the overall probability of getting a question correct was actually 0.6025.

The instructor setup a contingency table, sorting students based on whether they passed or failed, and whether they attended lecture live, only watched the recording, or only read the textbook (for the purpose of this question, assume that attending lecture, watching the recording, and reading the text are all mutually exclusive).

The instructor found that 40% of the students actually attended live lecture, and 2,200 students accessed the recording. There was a 97% chance of passing the test through if students attended lecture live. A total of 550 students who focused only on the textbook ended up passing the test. The probability of the recording wasn't given but it talks about it being mutually exclusive with the other conditions.

a. What percent of students passed the test?

b. What is the average grade?