There are seventyfive students in this class Each can earn e

There are seventy-five students in this class. Each can earn either an A, B, C, D, or F on the final exam. How many final exams must I grade to ensure that at least five students have received the same grade?

Solution

Total no of students 75

No of grades 5

If all grades are equally likely then

prob for each grade = 0.2

Expected no each grade = 75(0.2) = 15

If first grade is say K, then we must get another 4 grades in next 74 cases

Hence min grades should be 19 to get minimum 5 students have received same grade assuming probability and equal likely.