is it because there are more right handed people in the population as a whole so obviously more house hold accidents would be caused by right handed people because there are more of them as a whole?
The flaw in the argument is in equating probability and absolute numbers. It uses the fact that a bigger number of injuries are caused by righties to disprove the statement that lefties are more prone (probable) to cause injuries. But what matters is the relative sizes of the groups, so just because more injuries are caused by righties doesn't mean that they are more or less prone to cause them than lefties. We would have to know the number of accidents caused by each group relative to the size of each group to draw a probabilistic conclusion.
Your explanation is exactly right. Imagine there are 100 people in the world and 99 of them are right handed and 1 person (weirdo? :P) is left handed. You would totally expect that the right handed people would cause more accidents but that doesn't disprove the supposed myth. The one left handed dude could still be a total klutz. The argument doesn't account for frequency within the population.
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The flaw in the argument is in equating probability and absolute numbers. It uses the fact that a bigger number of injuries are caused by righties to disprove the statement that lefties are more prone (probable) to cause injuries. But what matters is the relative sizes of the groups, so just because more injuries are caused by righties doesn't mean that they are more or less prone to cause them than lefties. We would have to know the number of accidents caused by each group relative to the size of each group to draw a probabilistic conclusion.
Hope this helps!