How to show dropdown after selecting radio button using service?

I am not sure of the use case where you need to do it this way but this is how you can do it.

You can define a Validator function(bottom right Function -> +) which has a Boolean parameter & in the expression just enter the name of the same variable. Check Auto Evaluate checkbox. Save it.

Bind the State property of Radio button to this boolean parameter & the Output variable of the validator to the Visible property of Drop down.

When radio button is selected, true value will be set to the input variable and the same is being returned from the expression. So Output variable of validator is also true which in turn sets the Visible property of dropdown to true.