During the senior ‘All Night Grad Party" the student council wishes to raise money for the local food kitchen. They decided that having a raffle would be a good moneymaker. 100 tickets will be sold for $2
each. Three students will be selected to win $10 and the one grand prize winner will be $50. What is the
expected value for a student participating in this raffle? (in other words, how much can you expect to win or
lose by playing?)

After surveying students in her homeroom, katie decided to use a number cube to predict the probability that a randomly chosen student in her school planned to stay after school today for extracurricular activities. in katie’s simulation, a roll of 1 represents staying after school, while rolls of 2, 3, 4, 5, or 6 represent leaving school at the end of classes. according to katie’s model, what is the probability that three randomly chosen students will all stay after school for extracurricular activities today?