Probability of AccidentsLet
t
represent the total number of hours that a truck driver spends during a year driving on a certain highway connecting two cities, and let
p
(
t
)
represent the probability that the driver will have at least one accident during these
t
hours. Then,
0
≤
p
(
t
)
≤
1
, and
1
−
p
(
t
)
represent the probability of not having an accident. Under ordinary conditions, the rate of increase in the probability of an accident (as a function of
t
) is proportional to the probability of not having an accident. Construct and solve a differential equation for this situation.