Hi,

A school finds that 30% of the students are low achievers. The Headmaster is instructed to devise a revision module that will improve the situation. One hundred students are chosen at random and are given the revision module. 90% of high achievers pass the test and 20% of low achievers also pass.

(i) Based on these results, if a student chosen at random, takes the module, and passes it, determine the probability that he or she is a high achiever.

(ii) If the student fails the module, calculate the probability that he or she is a high achiever.