In particular, there are three news sources on the platform that are much more popular than all the other news sources that they host. We'll call these three sources N1, N2, and N3- Source N has probability .25 of being chosen when a user is selecting from Genre 1 and probability 0 of being chosen when a user is selecting from Genre 2. Source N has probability .2 of being chosen when a user is selecting from Genre 1 and probability .2 of being chosen when a user is selecting from Genre 2. Source N3 has probability .05 of being chosen when a user is selecting from Genre 1 and probability .3 of being chosen when a user is selecting from Genre 2. Now, for any user, we'll say that a source is the user's favorite if this source has a higher probability of being chosen by the user than any other source. Because these three news sources N, N2, and 3 are so much more popular than all other sources on the platform, we'll suppose that each user's favorite is one of these three. (That is, there are other news sources on the platform, but their probabilities are all so small that we don't need to think about them if our purpose is just to work out which is the favorite item of any given user.) Consider a user who has probability r of choosing from Genre 1 when they visit the platform, and a probability of 1-x of choosing from Genre 2. (Notice that this user always chooses something, since their probability of choosing from Genre 1 and their probability of choosing from Genre 2 add up to 1.) (2.1) (2 points) For which values of x is source N the favorite of a user with probability x of choosing from Genre 1 and probability of 1-x of choosing from Genre 2? Give an explanation for your answer. (2.2) (2 points) For which values of x is source N the favorite of a user with probability x of choosing from Genre 1 and probability of 1x of choosing from Genre 2? Give an explanation for your answer. (2.3) (2 points) For which values of x is source N3 the favorite of a user with probability x of choosing from Genre 1 and probability of 1x of choosing from Genre 2? Give an explanation for your answer. If you worked out the three previous questions correctly, then the correct set of x in each answer is an interval: it is the set of all that lie above some number a (the left endpoint of the interval) and below some larger number b (the right endpoint of the interval). (These pairs of endpoints a and b will be different for each of the three sources in your answers.) We'll call this set the interval from a to b. We can think of b-a, the distance between the endpoints, as the length of the interval. Suppose that both of these endpoints a and b are each > 0, and also each