Hi,
34 Students: 22 play football, 10 play basketball, and 5 play both.
See Venn Diagram: (22-5)only football and (10-5) only basketball
17 + 5 + 5 = 27 play one or both AND 34-27 = 7 play neither.
P(exclusively a basketball or a football player) = 22/34 = 11/17
P(neither a basketball nor a football player) = 7/34