Answer:
[tex]\frac{11}{20}[/tex]
Step-by-step explanation:
Total male students = 200
Students who play football (F)= 58
Students who play basketball (B)= 40
Students who play both (F∩B)= 8
The number of students who play either sport is
[tex](F\cup B)=F+B-(F\cap B)[/tex]
[tex](F\cup B)=58+40-8=90[/tex]
The number of students who play neither sport is
[tex]200-(F\cup B)=200-90=110[/tex]
The probability that a randomly selected male student plays neither sport is
[tex]Probability=\dfrac{\text{Number of students who play neither sport}}{\text{Total male students}}[/tex]
[tex]Probability=\dfrac{110}{200}[/tex]
[tex]Probability=\dfrac{11}{20}[/tex]
Hence, the required probability is [tex]\frac{11}{20}[/tex].
