Based on records of automobile accidents in a recent year, the Department of Highway Safety and Motor Vehicles in Florida reported the counts who survived (S) and died (D), according to whether they wore a seat belt (Y = yes, N = no). The data are presented in the contingency table shown.

a. What is the sample space of possible outcomes for a randomly selected individual involved in an auto accident? Use a tree diagram to illustrate the possible outcomes.
b. Using these data, estimate (i) P(D), (ii) P(N).
c. Estimate the probability that an individual did not wear a seat belt and died.
d. Based on part a, what would the answer to part c have been if the events N and D were independent? So, are N and D independent, and if not, what does that mean in the context of these data?

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Outcome of auto accident by whether subject wore seat belt Wore Seat Belt Survived (S) Died (D) Yes (Y) No (N) Total Total 412,878 164,128 577,006 510 412.368 162,527 574,895 1,601