Alexander Fleming was born on an Ayrshire farm. He left school at 15 and worked in a shipping office for 5 years until he inherited money from an uncle. On the advice of his brother Tom who was already a doctor he enrolled at St Mary’s Hospital, London in 1901.On qualifying with distinction in 1906 went to work with Sir Almroth Wright as an Assistant Bacteriologist. This retained him at Mary's, where he was a member of the rifle team.
In 1921 he accidentally sneezed on a culture plate and later noted that the bacteria on the plate had been killed. This led him to the discovery of the enzyme lysozyme produced by the body as a defence against infection.
In 1928 he was working with staphylococci and had left some culture plates uncleaned while he went on vacation. On return he noted that spores of the fungus Penicillium notatum had got onto one of the plates and that the mould had created a bacteria-free circle around itself. He reasoned that the mold had produced something which killed off the bacteria. After confirming this observation he named the substance Penicillin (as an improvement on his first description "mould-juice") but was unable to isolate it though he found that it killed other types of bacteria also. His work with Lysozyme had prepared him to regard the effect of the new substance as causing lysis which is reasonably accurate. He published his results in 1929.
Fleming, Florey and Chain were awarded the Nobel prize for medicine in 1945. 
The rules of the Nobel committee were such that a prize could be awarded to a maximum of three recipients.
The discoveries of lysozyme and penicillin are not an encouragement to careless laboratory practice, rather an encouragement to notice when things go wrong and ask why rather than just clear up the mess and carry on with the original work regardless.