Probabilities when events are independent (for example sampling with replacement). A useful formula: P(A and B) = P(A)*P(B) when events A and B are independent. A classroom has 5 first graders, 7 second graders, and 10 third graders. You are giving two prizes to students in the class (the same student can win both). You select a student at random to give the first prize and then select a student at random (from the whole class) for the second prize. What is P(both prizes go to third graders) = P(A and A) where A = event a 3rd grader is chosen