Two-thirds of papaya plants availabe are hermaphrodite and are self-pollinating. One-third of plants are female and need to be paired withh an hermaphrodite plant in order to be pollinated. Unless the plants are pollinated, they will not bear fruit. If you select three papaya plants at random, what is the probability that you will end up getting fruit? Meaning, what is the probability that you get at least one hermaphrodite plant?
what's the chance of getting no hermaphrodite plant? 1/3
So, I'd say the chance of getting no herms in 3 draws is 1/27, leaving 26/27 chance of getting at least one.
This assumes a large enough population that drawing 3 plants without replacement does not significantly affect the odds of the selections.