2 According to the U.S. Center for Disease Control, 20% of the U.S. population is infected with the herpes simplex-2 virus. Suppose a person has had three sex partners in their life. Develop a binomial probability distribution for the random variable X =# of partners out of three who were infected with this virus. a. Use the "Event Tree" approach to list all possible outcomes of having 3 partners who were either infected (1) or not infected (N) with this virus, and write the value of X corresponding to these outcomes for each. Event Tree Outcomes X P[Outcome] b. Use the multiplication rule to determine the probability for each of these outcomes, and write these probabilities to the right of the outcomes listed in the event tree. Note: If 20% of the population is infected, the probability that any randomly selected individual would be infected is P = 0.2 C. For each value X = # of infected partners out of three, write the number of different outcomes (combinations) that result in that value of X in the Table below. Sample space of X 0 2 # Combinations P[X] d. Use the addition rule to determine the probability associated with each value of X, based on the probabilities of outcomes and the number of combinations that result in each value of X. Enter these probability values in the Table above. e. Based on this probability distribution, determine the probability that a person who has had three sex partners was exposed to the herpes simplex-2 virus at least once, i.e., P [X 2 1]. (Hint: Review the Complement Rule of probability. There is an easy way to do this and a hard way) List all possible values of X that meet this criterion. Use the rules of probability to determine the probability of this event