Let's first find out how many play basketball (only), how many play baseball (only), and how many play both basketball and baseball.
There are 3 that do not play either sports, therefore, there are 27 - 3 = 24 students who play either baseball, basketball, or both.
Since there are 18 who play basketball and 16 who play baseball, there are 18 + 16 = 34 who play these sports.
But since there are only 24 players, some of these must play both.
34 - 24 = 10 -- which is the number who play both sports.
Removing these 10 students from the 18 who play basketball, there are 8 students who play only basketball.
Also, removing these 10 students from the 16 who play baseball, there are 6 student who play only baseball.
Summarizing:
There are 3 students who play no sports.
There are 8 students who play only basketball.
There are 6 students who play only baseball.
There are 10 students who play both basketball and baseball.
The probability that a student plays no sports is 3/27.
The probability that a student plays basketball (only) is 8/27.
The probability that a student plays baseball (only) is 6/27.
The probability that a student plays both sports is 10/27.
The probability that a student plays basketball is 18/27.
The probability that a student plays baseball is 16/27,