A university regularly conducts a satisfaction survey among its students. It uses the same questionnaire each year to measure satisfaction evolution. Students from Year 1 represent 45% of the total number, Year 2 students represent 35%, and Year 3 represent 20%.

Students in Year 1 have indicated a satisfaction of 85%; students from Year 2, 90%; and students from Year 3, 95%.

a. Develop a probability tree showing all marginal, conditional, and joint probabilities.

b. Develop a joint probability table.

c. What is the probability that a student selected at random is satisfied? ( LO,1)