1. A random sample of 400 State U faculty members was asked if they support a nosmoking ordinance on campus. Below are the data that also show their rank at the college. Adjunct Asst Assoc Full TOTAL --m --n \"unm- a. 'What is the probability a faculty member is an adjunct or supports the smoking ban? b. 'What is the probability a faculty member does not support the smoking ban given he/she is full professor? o. Are the events assistant professor and supports the smoking tum independent? Justify. 2. Suppose 73% of all Dairy King customers order a frozen treat during their visit, 42.5% order an item from the grill, and 33.15% do both. Calculate the following probabilities: a. A randomly selected customer orders a frozen treat or an item from the grill but not both. b. A randomly selected customer orders a frozen treat given he/she ordered an item from the grill. (3. Are the events orders a frozen treat and orders a. grill item. independent? Justify. 3. The student senate at State U comprises 28 members. Of these, 10 belong to the Young Republicans. Suppose a group of four student senators will be selected at random. \"that is the probability the group contains at least one member of the Young Republicans? Interpret this probability in context