An orthodontist has three financing packages, and each has a different service charge. He estimates that $10\%$ of

patients use the first plan which has a $$10$ finance charge; $10\%$ use the second plan which has a $$20$ finance charge;

and $80\%$ use the third plan which has a $$30$ finance charge. Complete parts a and $b.$

a$)$ Find the expected value of the service charge.

$E(x)=$$