the answer is (c)
After the vehicle is involved in a car accident or fire
Answer:
a) 
b) 
Explanation:
Previous concepts
The cumulative distribution function (CDF) F(x),"describes the probability that a random variableX with a given probability distribution will be found at a value less than or equal to x".
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution".
Part a
Let X the random variable of interest. We know on this case that 
And we know the probability denisty function for x given by:

In order to find the cdf we need to do the following integral:

Part b
Assuming that
, then the density function is given by:

And for this case we want this probability:

And evaluating the integral we got:

Answer:
(b)Distortion energy theory.
Explanation:
The best suitable theory for ductile material:
(1)Maximum shear stress theory (Guest and Tresca theory)
It theory state that applied maximum shear stress should be less or equal to its maximum shear strength.
(2)Maximum distortion energy theory(Von Mises henkey's theory)
It states that maximum shear train energy per unit volume at any point is equal to strain energy per unit volume under the state of uni axial stress condition.
But from these two Best theories ,suitable theory is distortion energy theory ,because it gives best suitable result for ductile material.