Respuesta :
Answer:
(a) P (Both vehicles are available at a given time) = 0.81
(b) P (Neither vehicles are available at a given time) = 0.01
(c) P (At least one vehicle is available at a given time) = 0.99
Step-by-step explanation:
Let A = Vehicle 1 is available when needed and B = Vehicle 2 is available when needed.
Given:
The availability of one vehicle is independent of the availability of the other, i.e. P (A ∩ B) = P (A) × P (B)
P (A) = P (B) = 0.90
(a)
Compute the probability that both vehicles are available at a given time as follows:
P (Both vehicles are available) = P (Vehicle 1 is available) ×
P (Vehicle 2 is available)
[tex]P(A\cap B)=P(A)\times P(B)[/tex]
[tex]=0.90\times0.90\\=0.81[/tex]
Thus, the probability that both vehicles are available at a given time is 0.81.
(b)
Compute the probability that neither vehicles are available at a given time as follows:
P (Neither vehicles are available) = [1 - P (Vehicle 1 is available)] ×
[1 - P (Vehicle 2 is available)]
[tex]P(A^{c}\cap B^{c})=[1-P(A)]\times [1-P(B)]\\[/tex]
[tex]=(1-0.90)\times (1-0.90)\\=0.10\times0.10\\=0.01[/tex]
Thus, the probability that neither vehicles are available at a given time is 0.01.
(c)
Compute the probability that at least one vehicle is available at a given time as follows:
P (At least one vehicle is available) = 1 - P (None of the vehicles are available)
[tex]=1-[P(A^{c})\times P(B^{c})]\\=1-0.01.....(from\ part\ (b))\\ =0.99[/tex]
Thus, the probability that at least one vehicle is available at a given time is 0.99.
