1. Tom rolls a number cube twice. What is the probability that the sum of the 2 rolls is less than 9, given that the first roll is a 6?
2. In a hospital ward, there are 16 nurses and 5 doctors. 3 of the nurses and 3 of the doctors are male. If a person is randomly selected from this group, what is the probability that the person is male or a doctor?
3. James believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request. He asked 500 students at his school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are shown in the table below:
Received math class requested: Honor roll= 315 --- Not on honor roll= 64 --- Total= 379
Did not get math class requested: Honor roll= 41 --- Not on honor roll= 80 --- Total= 121
Total: Honor roll= 356 --- Not on honor roll= 144 --- Total= 500
Help James determine if all students at his school have an equal opportunity to get the math class they requested. Show your work and explain your process for determining the fairness of the class assignment process.
4. Let A = {1, 2, 3, 4, 5} and B = {2, 4}. What is A ∩ B?