Researchers are interested in whether wearing seat belts protects against fatal injury in automobile accidents. They compiled the following data from all people involved in automobile accidents in the state of Florida: Fatal

Not Fatal

No Seat Belt

1,581

161,227

Seat Belt

588

412,368

Using these data, calculate

a. The simple probability that a seat belt is not worn.

b. The simple probability that a fatal injury occurs.

c. The probability that both a fatal injury occurs and a seat belt is not worn

P(Fatal injury ∩ No Seat Belt)

d. The probability of a fatal injury or that the seat belt was not worn or both.

P(Fatal injury U No Seat Belt)

e. The conditional probability that a fatal injury occurs given that a seat belt was not worn.

f. Is the event of having a fatal injury independent of not wearing a seat belt?

(show your work).

My answer so far but im completly stuck on f:

Fatal Not Fatal Total
No Seat Belt 1,581 161,227 162,808
Seat Belt 588 412,368 412,956
Total 2,169 573,595 575,764
a. 162808/575764= 0.282769
b. 2169/575764= 0.003767
c. 1581/162808= 0.009711
d. (2169+162808-1581)/575764= 0.28379
e. (0.003767*.009711)/0.009711= 0.003767
f.