Answer:
0.0114
Step-by-step explanation:
(a) What is the probability of a fatal accident over a lifetime?
Suppose A be the event of a fatal accident occurring in a single trip.
Given that:
P(1 single auto trip in the United States result in a fatality) = P(A)
Then;
P(A) = 1/4011000
P(A) = 2.493 × 10⁻⁷
Now;
P(1 single auto trip in the United States NOT resulting in a fatality) is:
P([tex]\mathbf{\overline A}[/tex]) = 1 - P(A)
P([tex]\mathbf{\overline A}[/tex]) = 1 - 2.493 × 10⁻⁷
P([tex]\mathbf{\overline A}[/tex]) = 0.9999997507
However, P(fatal accident over a lifetime) = P(at least 1 fatal accident in lifetime i.e. 46000 trips)
= 1 - P(NO fatal accidents in 46000 trips)
Similarly,
P(No fatal accidents over a lifetime) = P(No fatal accident in the 46000 trips) = P(No fatality on the 1st trip and No fatality on the 2nd trip ... and no fatality on the 45999 trip and no fatality on the 46000 trip)
= [tex][P(\overline A)] ^{46000} \ \ \ (since \ trips \ are \ independent \ events)[/tex]
= [tex][0.9999997507]^{46000}[/tex]
= 0.9885977032
Finally;
P(fatal accident over a lifetime) = 1 - 0.9885977032
P(fatal accident over a lifetime) = 0.0114022968
P(fatal accident over a lifetime) ≅ 0.0114
