Suppose 3% of the population is infected by a virus. A medical test for infection was developed that returns a positive result 75% of the time on people who are infected; • returns a negative result 95% of the time on people who are healthy. Compute the probability that (i) a person is infected given they tested positive; (ii) a person is healthy given they tested negative.

In the sport of basketball, a player will sometimes get the opportunity to shoot two free throws without being affected by any other players in the game.  Assume that, for one player, these two free throws are independent of each other.  If this player makes free throws 80% of the time, what is the probability that this player will make neither free throw in the opportunity?

A recent survey showed that 94 adults out of a sample of 500 have high blood pressure. However, 108 of those studied reported being unwilling to change their diet. Based on this sample, if an adult is chosen at random, what is the probability that he or she is open to trying to eat more healthfully? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Suppose the sensitivity of a diagnostic procedure to test whether a person has a particular disease is 95 % . A person who actually has the disease is tested for it using this procedure by two independent laboratories. (1) What is the probability that both test results will be positive? (ii) What is the probability that at least one of the two test results willI be positive?