Half of the 20 students play basketball, so there are 20/2 = <<20/2=10>>10 students who play basketball.
Two-fifths of the 20 students play volleyball, so there are 20 * 2/5 = <<20*2/5=8>>8 students who play volleyball.
One-tenth of the 20 students play both basketball and volleyball, so there are 20 * 1/10 = <<20*1/10=2>>2 students who play both games.
To find the number of students who do not play either game, we can subtract the total number of students who play basketball or volleyball from the total number of students.
The total number of students who play basketball or volleyball is 10 + 8 - 2 = <<10+8-2=16>>16 students.
Therefore, the number of students who do not play either game is 20 - 16 = <<20-16=4>>4 students.
#### 4
The answer is: 4
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Out of the 20 students in the class, half of them play basketball, two-fifths play volleyball, and one-tenth play both basketball and volleyball. What is the number of students in this class who do not play either game?

### Answer:
