In deciding what precautions to take, the hypothetical "reasonable person" (whether engaged in a skilled activity or not) will take various factors into account. These may include the degree of risk, the seriousness of the consequences if an accident does happen, the cost and practicality of guarding against the risk, and the social importance of the activity in question.
The probability of harm is certainly relevant, so in Fardon v Harcourt Rivington (1932) 146 LT 391 Lord Dunedin said that while people were expected to guard against reasonable probabilities, they were not bound to guard against fantastic possibilities.
Bolton v Stone  1 All ER 1078, HL
Miss Stone, standing on the pavement outside her house, was struck by a cricket ball hit from an adjacent cricket ground. The ball must have travelled about 100 yards, clearing a 17-foot fence, and such a thing had happened only about six times in thirty years. P's claim for damages was rejected by the House of Lords: the risk was so slight and the expense of reducing it so great that a reasonable cricket club would not have taken any further precautions.
Cameron v Hamilton's Auction Marts  SLT 74, Sheriff Court (Scotland)
The court decided there was no liability in a case where a cow entered an open door, walked upstairs, and turned on taps, flooding the floor below: this was so improbable that no reasonable person would have taken any precautions against it.
Hilder v Associated Portland Cement  3 All ER 709, Ashworth J
DD were the owners of waste ground, and they allowed children to play football on that ground. At one end, there was a three-foot wall behind the "goal", and balls were commonly kicked into the road. One such ball struck a passing motor-cyclist, causing him to crash and be killed. The motor-cyclist's family sued, and the owners of the land were found liable in negligence. A reasonable landowner would have seen the risk to passing motorist, and given the frequency with which balls went into the road the risk was not so small that it could be ignored.
Roe v Minister of Health  2 All ER 131, CA
Two patients were paralysed by a spinal anaesthetic that had become contaminated through invisible cracks in the glass vial. It was established by evidence that the cracks were not foreseeable given the scientific knowledge of the time, and the Court said DD were not liable. The foreseeability of harm is clearly a major factor in determining how a reasonable person would act, and although actual foresight by D is generally irrelevant, a reasonable person would not have taken precautions against a risk of which reasonable people in that profession were not aware.
Gunn v Wallsend Engineering (1989) Times 23/1/89, Waterhouse J
The wife of a shipyard worker contracted mesothelioma from asbestos dust in her husband's clothes, which she had handled and shaken out before washing them. Her action for damages against the shipyard failed, since at the time (before 1965) the risk was unforeseeable. No one in the industrial world directed his mind to the risk of physical injury from indirect domestic exposure to asbestos dust, and there was no medical literature or official guidance on the subject. A prudent employer would not have foreseen the risk, and so could not be expected to guard against it.