Four people are seated around a table as in the diagram below. Another clumsy person accidentally spills water on two adjacent people at the table. (For example, the water could be spilled on 1 and 2, or on 1 and 4, but not on 1 and 3.) The clumsy person is equally likely to spill water on any of the four adjacent pairs. 4 2 Let W₁ be the event "person 1 had water spilled on them". Define W2, W3, W4 similarly. (a) Which pairs of the events W₁, W2, W3, W₁ are independent? Explain why. (b) Which pairs of the events W₁, W2, W3, W4 are disjoint? Explain why.

T1.2 A person entering a university building is a student (S), faculty (F), or staff (W). We observe three successive persons entering the building. a) List all outcomes in the event A that exactly two are students. b) List all outcomes in the event B that the third person is a faculty

This student never eats the same kind of food for 2 consecutive weeks. If she eats a Chinese restaurant one week, then she is five times as likely to have Greek as Italian food the next week. If she eats a Greek restaurant one week, then she is four times as likely to have Chinese as Italian food the next week. If she eats a Italian restaurant one week, then she is twice as likely to have Chinese as Greek food the next week. Assume that state 1 is Chinese and that state 2 is Greek, and state 3 is Italian. Find the transition matrix for this Markov process. P = 出 出 曲

In a soon to be released Halloween martial arts movie, a pumpkin has a starring role. Because of the rather violent nature of the film, the producers have also hired a stunt pumpkin.  Suppose the featured pumpkin appears in 40% of all the film scenes, the stunt pumpkin appears in 30% of the film scenes and the two appear simultaneously in 5% of the scenes. Draw the Venn diagram to reflect information given in the problem. Are the events the stunt pumpkin appearing in a scene and the featured pumpkin appearing in a scene mutually exclusive (disjoint)? Explain how you know. Are the events the stunt pumpkin appearing in a scene and the featured pumpkin appearing in a scene independent? Explain how you know. What is the probability that in a given scene that only the stunt pumpkin appears?   You have three events A, B, & C. Suppose: Event A is the event of drawing a king from a deck of 52 cards on the first draw. Event B is the probability of drawing a queen of hearts on the…