Understanding statistics Speaker on the Christian channel said he read an article that said: "We asked 5000 random women if they experienced domestic abuse; 1,000 said yes." Therefore, the article went on, we predict 1 woman in 5 will experience domestic abuse.
He then said, "Boy, am I steamed because I have 5 daughters!"
Is he correct in lamenting that one of his five daughters is certainly going to experience domestic abuse? Or does his understanding of statistical significance need to be improved? Does he realize that generally speaking, overall. Is he familiar with the 'law of large numbers?'
Is his statement "Boy, I'm steamed" ridiculous and silly?
 A: I think the speaker was probably making a joke, playing on the fact that statistical averages do not accrue with certainty.  There are plenty of reasons that this conclusion would not accrue statistically.
Even if it is true that 1-in-5 present females experience domestic abuse (and you would want to look a lot more closely at the details of the research before accepting this), the speaker's daughters are not "random women" - they are women with specific characteristics that would make them more or less likely than average to experience domestic abuse (almost certainly less likely, given what we know about them just from the question).  Moreover, rates of domestic abuse may also change over their lifetime; since the current trend is downward, one might reasonably expect that trend to continue, so that the probability of even an average woman experiencing domestic abuse might end up being less than the outcome of this point-in-time survey.
Getting a realistic estimate of the probability that a given one of his daughters will experience domestic abuse, would be a difficult exercise.  Even if individual probabilities could be estimated, this would still mean that the number of his daughters that experience domestic abuse will be a random variable with a particular distribution.  Even if the expected value of this distribution is one, this does not mean that it is certain that exactly one of his daughters will experience abuse.
