Question 126741
If we say that the probability of {{{no}}}{{{ fatal}}} accidents in a lifetime is {{{P}}} and the probability of having one (or more) {{{fatal}}} accidents in a lifetime is{{{p}}}, then we have:

{{{p=1-P=1-(3999999/4000000)^50000 =0.0124}}} (or about {{{1.2}}}%)

-or {{{1 - p =P}}} that is the probability that you survive each and every journey

a)

Why the independence assumption might be violated?

hmmm, that is more question of “psychology” then statistics

-overconfidence, less care when driving, doing other things in same time, and 

so on, could cause {{{p}}} 

(b) Why might a driver be tempted not to use a seat belt “just on this trip”?

it might be he/she was thinking about {{{P}}}....
(:-))))

many drivers think "it didn't happened to me never before, so it shouldn't happen now too"