There is nothing wrong with noticing an odd event and asking the question "why?" and there is nothing wrong with having a bit of luck. It happens all the time.
Louis Pasteur said: "Dans les champs de l'observation, le hasard ne favorise que les esprits preparés." ("In observation, chance favours only the prepared mind.").
Louis Pasteur used dead cholera germs to infect poultry by mistake. Then he injected the birds with live bacteria but found they were now protected in some way.
Louis Pasteur looked at the inactive form of tartaric acid under the microscope, and saw that it was made up of two sorts of crystals with mirror-image forms.
Pasteur separated out the two crystal types with tweezers, tested them, and found the solution made from one group was optically active in the expected way.
Pasteur also found that a solution of tartaric acid crystals from the other group turned light the opposite way, introducing us to the idea of isomers.
James Clerk Maxwell's experiment in colour photography only worked because the red dye in the tartan he photographed reflected UV, and the film detected it.
Henri Becquerel might have missed radioactivity if bad Paris winter weather had not caused him to leave uranium salts and photographic paper in a drawer.
If Alexander Fleming had not misclassified penicillin as a lytic agent, Howard Florey and Chain may not have chanced upon it when they made a literature search.
If Alexander Fleming had not used bad technique near where La Touche was culturing some unusual Penicillium, he would never have seen the penicillin effect.
When Clinton Davisson and Lester Germer demonstrated electron diffraction by a crystal, it only worked because they had dropped and damaged their equipment.
This file is http://members.ozemail.com.au/~macinnis/scifun/splatserendip.htm, first created on February 16, 2008. Last recorded revision (well I get lazy and forget sometimes!) was on February 16, 2008.