(b) That's wrong. To answer this question, you should recall that terms become part of a contract not only by agreement, but also by operation of law. This means that even if Peter did not promise (either expressly or impliedly) to use due care and skill, such a duty might still become part of the contract because the law puts that term into such contracts (generic terms). You should recall, for example, that in a contract between a doctor and a patient, it becomes a term that the doctor will use due care and skill. See Breen v Williams.
Such terms are also implied into other contracts for professional services. It is therefore likely that a court would find that a qualified electrician who undertakes an electrical installation would be required to exercise due care and skill. By failing to check the wiring before connecting the power, Peter has not taken proper care. By connecting the wire wrongly, he has not exercised proper skills.
Accordingly, (a) is a better answer than (b).
The third answer (c) is not a good choice because, while it correctly states that even qualified persons can make mistakes, that in itself does not justify the conclusion that there can be no breach of contract. If, by making a mistake, the person concerned is failing to perform the work in the way required by the terms of the contract, then there will be a breach of contract.