There are 55 student in eight grade middle school that play different sports. 27 of them play soccer, 15 of them play basketball. 11 of them play soccer or basketball. What is the probability given that the they are in eight grade and play sports that they play both soccer and basketball?

11/55 = ?

To find the probability that a student plays both soccer and basketball, we need to consider the number of students who play soccer, the number of students who play basketball, and the number of students who play both.

According to the given information, there are 27 students who play soccer, 15 students who play basketball, and 11 students who play soccer or basketball.

To find the number of students who play both soccer and basketball, we can subtract the number of students who play only soccer from the total number of soccer players, and similarly subtract the number of students who play only basketball from the total number of basketball players.

Let's calculate them:

Number of students who play only soccer = Number of soccer players - Number of students who play both soccer and basketball
= 27 - 11
= 16

Number of students who play only basketball = Number of basketball players - Number of students who play both soccer and basketball
= 15 - 11
= 4

Now, let's find the number of students who play both soccer and basketball:
= Number of students who play soccer + Number of students who play basketball - Total number of students who play sports
= 27 + 15 - 55
= 42 - 55
= -13

Since we have a negative value, it means there is an error in the given information or it is not possible for any student to play both soccer and basketball.

Therefore, the probability of a student in eighth grade playing both soccer and basketball cannot be determined accurately based on the given information.