Suppose that over the past several years, 4,000 students have taken a certain course, which has a midterm test. Suppose also that 85% passed the test, 95% of those who passed the test also passed the...

Suppose that over the past several years, 4,000 students have taken a certain course, which has a midterm test. Suppose also that 85% passed the test, 95% of those who passed the test also passed the course, and 92% of those who failed the test also failed the course.

(a) Construct a contingency table.

(b) If one of those students were selected at random, calculate to 5 decimal places:

(i) prob(he failed the test j he passed the course)

(ii) prob(he passed the test j he failed the course)