It was statistical thinking like this that got some of the questionable cot death convictions, originally the doctors said that the chances of two siblings dying from cot death were so far out that it had to be murder, Lightning doesn't strike the same place twice and all that.Just playing around with statistics a bit more (and assuming of course that the seller was not the sort of company which would return the duds to stock!) if a company sold 1500 batteries in a year, I make it that you would expect to see one customer getting a dud first time followed by a dud replacement (ie Tillson's experience), once a year if 39 out of the 1500 were found by customers to be duds. That would be a dud rate of 2.6%.
To be honest, that's probably not too bad a failure rate, and shouldn't, in itself, put people off buying a Kalkhoff. But if Tillson get's a third dud, or more examples emerge of people getting two duds, the failure rate would climb.
Later on good reasons were found that cot deaths are far more likely to happen in a household where it has happened before, the convictions were overturned.
What I'm trying to say is that we don't know why the batteries failed but once he has one fail then he is much more likely to experience a second failure. For all we know the battery could have been kept next to an ultrasound device which changed the insides, or a microwave oven that leaked microwaves. All very small chances but still important when considering freak statistics.