A student takes a true-false test. There are 12 questions on the test, of which he knows the answer to 4.
What are the chances of passing this test? (assuming that 50% is a pass).
How would i set this equation up?
He needs 6 correct answers to pass and he already has 4. That means he needs 2 more to pass. It's easier to look at how he can fail. That means no correct answers or only 1 correct answer. The probabilities are:
Probability of no correct answers:
8 choose 0 (1/2)^8
Probability of 1 correct answer:
8 choose 1 (1/2)^8
Add these 2 up, subtract the result from 1 and you have the probability he has 2 or more correct answers.