A board game spinner has 7 equally likely areas numbered 1, 2, ..., 7. a) The spinner is spun twice. What is the probability that at least one spin lands on the number 6? b) The spinner is spun twice. What is the probability that the sum of 8 or 11 (the sum of the 2 spins) occurs if you are told that the first spin landed on the number 5? c) The spinner is spun 7 times. What is the probability that the spinner lands on each of the seven numbers? 63% of adults surveyed like to eat eggs for breakfast, 38% like to eat bacon and 29% like to eat both. A Venn diagram may be helpful in answering the following questions. a) Given that a randomly selected adult from the survey likes eating eggs, find the probability that they do not like to eat bacon. b) Given that a randomly selected adult from the survey likes to eat at least one of these two types of food, find the probability that they like to eat eggs. The front row of Room 8 Sutherland has 12 seats. If five computer scientists, three mathematicians, and four historians are to sit in the front row of Room 8, what is the probability that the mathematicians do not sit next to each other.