Answer
$P(E)=0.6$
Work Step by Step
Event = "John stays home" = {Roberto and Clarice, Roberto and Dominique, Roberto and Marco, Clarice and Dominique, Clarice and Marco, Dominique and Marco}. So, $N(E)=6$.
The sample space: S = {John and Roberto, John and Clarice, John and Dominique, John and Marco, Roberto and Clarice, Roberto and Dominique, Roberto and Marco, Clarice and Dominique, Clarice and Marco, Dominique and Marco}. So, $N(S)=10$.
Using the Classical Method:
$P(E)=\frac{N(E)}{N(S)}=\frac{6}{10}=0.6$