Updating checkbox by ajax in jsf

I have problem with refreshing checkbox in jsf. I have code:

<p:selectBooleanCheckbox disabled="#{not bean.selected}"/>

I'm changing selected value in application and when I'm doing that I'm trying update that checkbox. I have to use ajax. I know, there is "update" method but I don't know how to use it. Should I use update=":checkboxID"?