statistics and Probability

'3 '1 ' A certain disease has an incidence rate of 0.4%. If the false negative rate is 6% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease. A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 8% of the time if the person does not have the virus. (This 8% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive\". a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A| BI= % b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A'| 3'). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A'| B') = A boy owns 5 pairs of pants, 6 shirts, 6 ties, and 8 jackets. How many different outfits can he wear to school if he must wear one of each item? How many different ways can a race with 6 runners be completed? (Assume there is no tie.) In how many ways can first, second, and third prizes be awarded in a contest with 135 contestants? In how many ways can 5 books be choosen from a group of nine? From a group of 7 people, you randomly select 2 of them. What is the probability that they are the 2 oldest people in the group? Give your answer as a fraction You pick 3 digits (0-9) at random without replacement, and write them in the order picked. What is the probability that you have written the first 3 digits of your phone number? Assume there are no repeats of digits in your phone number. Give your answer as a fraction. In a lottery game, a player picks six numbers from 1 to 20. If the player matches all six numbers, they win 50,000 dollars. Otherwise, they lose S1. What is the expected value of this game? A bag contains 3 gold marbles, 10 silver marbles, and 21 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game