A blood test for diabetes gives a positive result with a proportion of 0.83 when an individual has diabetes and a negative result with a proportion of 0.81 when they do not. Approximately a proportion of 0.89 of the population has diabetes. If a randomly chosen citizen tested negative, what is the probability that they actually have diabetes? Round your answer to five decimals. Answer: Zoonotic disease outbreaks are infectious disease outbreaks in humans that are caused by pathogens from wild or domesticated animals. Suppose two pathogen genotypes occur in chickens, and one of them is accidentally transmitted to a farmer, each being selected with probability 0.22 for type 1 or 0.78 for type 2. If type 1 is transmitted, then an outbreak will occur with probability 0.82, whereas if type 2 is transmitted, then an outbreak will occur with probability 0.19. What is the overall probability of an outbreak? Round your answer to five decimal places. A probability density function for the random variable X is given by pi = ki, where k is a constant. What value must k be if X takes on integer values between 0 and 39? Round your answer to five decimal places. Answer: Consider the following card game with a well-shuffled deck of cards. If you draw a red card, you win nothing. If you get a spade, you win $74.55. For any club, you win $14.94 plus an extra $76.99 for the ace of clubs. What is the expected value of your winnings if you play the game? Round your answer to five decimal places. Answer: Dengue-fever viruses are carried by mosquitoes. There are several different serotypes of the dengue virus, and one study showed that, of all mosquitoes that carried serotype A, a proportion of 0.41 also carried serotype B. If the proportion of serotypes A and B in the mosquito population are 0.4 and 0.91, respectively, what is the probability that a randomly selected mosquito carrying serotype B also carries serotype A? Round your answer to five decimal places.