Thanks to our confirmation bias, in which we look for and find confirmatory evidence for what we already believe and ignore or discount contradictory evidence, we will remember only those few astonishing coincidences and forget the vast sea of meaningless data.
We can employ a similar back-of-the-envelope calculation to explain death premonition dreams. The average person has about five dreams a night, or 1,825 dreams a year. If we remember only a tenth of our dreams, then we recall 182.5 dreams a year. There are 300 million Americans, who thus produce 54.7 billion remembered dreams a year. Sociologists tell us that each of us knows about 150 people fairly well, thus producing a social-network grid of 45 billion personal relationship connections. With an annual death rate of 2.4 million Americans, it is inevitable that some of those 54.7 billion remembered dreams will be about some of these 2.4 million deaths among the 300 million Americans and their 45 billion relationship connections. In fact, it would be a miracle if some death premonition dreams did not happen to come true!
Imagine what our society would be like if we did have an accurate, natural intuition about probabilities. Magnet healing would no longer be a viable business and poker would get much, much more competitive.