A bag contains beads, 60% of which are green. A student claims that the probability of getting two green beads if the beads aren't replaced is 1/3 as 6/10 * 5/9 is 1/3. Is the student right?

They have multiplied the fractions correctly but they are still incorrect. The student has assumed that a bag with 60% green beads contains 10 beads. If the bag had 100 beads and 60 were green, 60% of the beads would still be green but the probability of both being green is no longer 1/3, therefore the student is wrong.