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The school finds that 30% of the students are low achievers. The Headmaster is instructed to...

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

Based on these results, if a student chosen at random, takes the module and passes it, what is the probability that he or she is a high achiever? If the student fails the module, what is the probability that he or she is a high achiever?

Math   Statistics-And-Probability   
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Answer #1

Define the events ,

The following probabilities are defined . Using complementary probability

Using conditional probabilities,

The conditional probability,

probability that he or she is a high achiever given he/she passes the test is

probability that he or she is a high achiever given he/she fails the test is

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