Interesting problem--if indeed related to business.
Assuming that it is, I believe an answer might be as follows:
First, let the first truck's availability be event A and the
availability of the second truck be event B. From your info, then, we
are provided with P(A) =0.75 & P(B)= 0.5. Now, if events A & B were
mutually exclusive(i.e., independent from each other), then the
probability of both event A and event B occuring together, P(AB),
would be
P(AB)=P(A)P(B)
And conversely, P(A'B')=P(A')P(B')
Where A' = Event of Nonavailability of First Truck
B' = Event of Nonavailability of Second Truck
A'B' = Event of neither the First and Second Truck being available
And P(A') = 1 - P(A)
P(B') = 1 - P(B)
However, since P(AB) = 0.3 (as given), then we know that these events
are not independent from one another (perhaps they share the same
maintenance resources,etc.) and we must pursue another path.
Consider the following:
P(A) = P(AB) + P(AB')
P(A') = P(A'B) + P(A'B')
P(B) = P(AB) + P(A'B)
P(B') = P(AB') + P(A'B')
Solving for P(AB') using the first equation yields:
0.75 = 0.3 + P(AB')
P(AB') = 0.45 (Note: This is the probability of the First truck being
available and the Second truck not being available concurrently)
Further, as P(B') = 1 - P(B), then P(B') = 1 - 0.5 = 0.5
Solving for P(A'B') yields:
0.5 = 0.45 + P(A'B')
Therefore,
P(A'B') = 0.05
Thus, the probability that neither the first and second truck will not
be available is 5%. |