For parts $($a$)($d$),$ suppose that a resident of the United States is selected at random. For each of the following pairs, indicate which probability is larger. $($Circle your answer; do not bother to explain.$)$

$($a$)$ A$.$ P$($lives in SLO county $|$ lives in California$)$

B$.$ P$($lives in California $|$ lives in SLO county$)$

$($b$)$ A$.$ P$($has a pet $|$ lives in California$)$

B$.$ P$($lives in California $|$ has a pet$)$

$($c$)$ A$.$ P$($lives in California and has a pet$)$

B$.$ P$($lives in California or has a pet$)$

$($d$)$ Chloe is $27$ years old, single, and very bright. As a student, she was deeply concerned with issues of discrimination and social justice and also participated in anti$-$nuclear demonstrations. Which probability is larger?

A$.$ Chloe majored in philosophy

B$.$ Chloe majored in philosophy and has a cat.