Thread: Probability Help!

Suppose that it is known that in an entrance exam, 10% cheat on the exam, and 90% do not. About 70% of the cheaters get a perfect score, while 20% of the noncheaters get a perfect score.

1) What is the probability that a randomly selected student taking the exam will get a perfect score?
2) Give that a student has a perfect score on the exam, what is the conditional probability that it was obtained by cheating?

Originally Posted by rafaeli

Suppose that it is known that in an entrance exam, 10% cheat on the exam, and 90% do not. About 70% of the cheaters get a perfect score, while 20% of the noncheaters get a perfect score.

1) What is the probability that a randomly selected student taking the exam will get a perfect score?
2) Give that a student has a perfect score on the exam, what is the conditional probability that it was obtained by cheating?

Try drawing a tree diagram to see that:

1) (0.1)(0.7) + (0.9)(0.2) = ....

2) (0.1)(0.7)/[(0.1)(0.7) + (0.9)(0.2)] = ....