1.) An experiment consists of selecting one of two urns and then removing a marble from the urn. Urn I contains 19 violet marbles and 13 white marbles. Urn II contains 17 violet marbles and 8 white marbles. Assume that the urns are equally likely to be selected. Find the probability that A marble was selected from Urn I, if it is known that the marble is violet.
2.) About 8.3% of the American population has diabetes. A combination of blood tests accurately diagnoses diabetes 99.3% of the time. The tests give false positive results for 1.2% of people who do not have the diabetes. Find the probability that . The blood tests show that a person has diabetes.
3.) Urn 1 contains 14 green and 15 yellow marbles. Urn 2 contains 11 green and 8 yellow marbles. An experiment consists of choosing one of two urns at random then drawing a marble from the chosen urn. Urn 1 is more likely to be chosen than Urn 2 with probability 0.57.
What is the probability that a green marble was chosen?
What is the probability that Urn 1 was chosen, if it is known that a yellow marble was drawn?
4.) A television manufacturer has three locations where it is final ly assembled. Plants A, B, and C supply 65%, 15%, and 20% respectively of the televisions used by the manufacture. Quality control has determined that 1.5% produced by Plant A are defective, while plants B and C have 2.5% defective products.
What is the probability of finding a non-defective television?
What is the probability that the television was manufactured by Plant B, given it was defective?
5.) At a carnival you win a prize if you get a heads, you must first choose a coin. There is a fair and a biased coin, while choosing each coin is equally likely, the biased coin has a 78% of landing tails. What is the probability of choosing the biased coin if you won a prize?