Basic statistics, calculating odds over time Given the data that in 2016 4.6 million people were seriously injured in car accidents I came up with the following over time assuming nothing else changes: 4.6M injured / 330M total population = 1.39% yearly risk of injury 1.39% risk of injury x 80 years avg lifespan = 111.5% risk of injury But it is recommended to do it this way with the odds of not being injured: (1 - 0.0139) ^ 80 = 32.6% making the chance of serious injury 67.4% over 80 years. Why does the first way not work?

What you have calculated is the average number of injuries over 80 years. If every year you have a probability of 0.0139 of getting injured, the average number of injuries you will sustain in 80 years is $80 \times 0.0139 = 1.112$. On the other hand, the probability of not getting injured at all in 80 years is the product of the probabilities of not getting injured in year 1, year 2, ..., year 80 (assuming that these events occur independently), which is $(1-0.0139)^{80}$.

I recommend reading up on the binomial distribution.