If I hire an electrician to do some job, and he caused a fire at the house. Am I also somehow legally responsible for the accident because I hired him and not another electrician, who might have been more competent and avoided the accident? Or I am not responsible at all?
There are various ways in which you could be "responsible". For example, if you own the house, have no insurance, the house burns to the ground and the electrician has no resources that you can seize, then you will have to suffer the consequence of having no home. If a guest is harmed in the fire, you might be found liable because of your negligence (plaintiff's lawyer has to put convincing spin on your actions in showing that you neglected your duty of care). Since you are hiring the electrician, under the doctrine respondeat superior you can become liable for the worker's acts carried out on the job. What matters in that case is how the act came to be, for example did it happen as a result of bad wiring that he was hired to do, or was he a crazy arsonist who look advantage of an opportunity to torch your house (you are not liable, torching the house is not an act reasonably related to what you hired him for).
You could end up responsible for the loss if you are insured, the "electrician" was uninsured (and other kinds of "un" like "unlicensed"), and the insurance contract allows the claim to be denied because you wrongly hired an unqualified, unlicensed guy off the street who did not secure the required permits. That doesn't mean that you can't sue him, but if you cannot collect on the judgment, then you end up having to take responsibility for your action.
"Responsibility" is a legally vague concept, instead I assume you are interested in whether the courts might force you to pay for the damage done to someone, or even might punish you for a criminal act. In the former case, the relevant legal concept is "liability", meaning that you can be required to compensate another for the damage that you caused. In the latter case, the criteria are much stricter, that you have to deliberately do a thing that was explicitly forbidden.