Suppose that 52% of all students on campus wear glasses. If two students are chosen at random, what is the probability that both of them wear glasses?

Question

Suppose that 52% of all students on campus wear glasses. If two students are chosen at random, what is the probability that both of them wear glasses?

Give the answer as a decimal proportion, with 3 decimal places.

Answer 1

(.52)^2 =(52/100)(52/100) = .2704 = .270 rounded off to 3 decimal places = 27% chance both wear glasses

That's assumer a "large" number of students.

But if there were a relatively "smaller" number such as a total 50 students with 26 wearing glasses

then the probability would be (26/50)(25/49) = .2653 = .265 founded off to 3 decimal places = 27% chance both wear glass rounded of to nearest integer precent.

the larger the total number of students the closer to exactly 27% probability