Since, A and B are independent events
$\therefore\text{P}(\text{A}\cap\text{B})=\text{P}(\text{A}).\text{P}(\text{B})$
$\text{P}\big(\frac{\text{A}}{\text{B}}\big)=\frac{\text{P}(\text{A}\cap\text{B})}{\text{P}(\text{B})}=\text{P}(\text{A})$
and $\text{P}\big(\frac{\text{B}}{\text{A}}\big)=\frac{\text{P}(\text{B}\cap\text{A})}{\text{P}(\text{A})}=\text{P}(\text{B})$
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