Probability Homework Problems(1) Rolling three distinguishable dice (e

Probability Homework Problems(1) Rolling three distinguishable dice (e

Probability Homework Problems(1) Rolling three distinguishable dice (e.g., assume that there is a way to tell them apart, for instance, that the dice are three different colors). Let Bk be the event that the maximum value that appears on all three dice when they are rolled is less than or equal to k. Find P(B1), P(B2), P(B3), P(B4), P(B5), and P(B6). Keeping the set-up the same, give a general formula for P(Bk).(2) A student buys a brand new probability textbook that has 500 pages, numbered from 1 to 500. She randomly opens the book to a page and starts to read. Assume that any of the 500 pages are equally likely to be chosen. Using inclusion and exclusion to find the probability that the page number she chooses contains at least one 5 as a digit. Keeping the set-up the same, what is the probability that the page number contains at least on 3 as a digit.(3) Consider a well-shuffled deck of 52 cards, and draw at random three cards. What is the probability that at least one is an ace?(4) Suppose that there are four restaurants in Chicago that have the same name, Sweet House. Four students are going to meet at Sweet House. If each student chooses a restaurant at random, calculate the probability that: i) All four choose the same restaurant; ii) All four choose different restaurants.(5) Assume that events A1, A2, and B1 are independent and the events A1, A2, and B2 are independent. Also assume that B1 and B2 are disjoint. Prove or disprove the events A1, A2, and B1 ? B2 are independent.(6) Roll a die. Let A be the event that the outcome on the dice is an even number. Let B be the event that the outcome on the dice is 4 or smaller. Let C be the event that the outcome on the dice is 3 or larger. Are A and B independent? Are B and C independent?