Answer:
(1) Pr(A > B + C) = 0
(2) [tex]\mathbf{\dfrac{1}{27}}[/tex]
Step-by-step explanation:
From the information given:
What is the probability A is the last customer to complete service when:
(1) the service time for each clerk is precisely ten minutes?
The probability (Pr) that A is the last customer can be computed as:
P( A > B + C )
if we recall, we are being told that the service time for each clerk is 10 minutes. As such, there is no occurrence of any event.
Therefore, the probability A is the last customer to complete service when the other customers had left will be :
Pr(A > B + C) = 0
(2) when the service time are (i) with probability(pr) 1/3, i=1,2,3?
when service time i are (1,2,3) with probability [tex]\dfrac{1}{3}[/tex]
Then the event that A will be the last customer to complete service when the other two customers had left will occur when A = 3, B= 1, C= 1
Thus, the probability that A is the last customer to complete service when the other customers had left will be :
Pr ( A > B + C ) = Pr( A = 3, B = 1, C = 1)
Pr ( A > B + C ) = [tex]\begin {pmatrix} \dfrac{1}{3} \end {pmatrix}^3[/tex] given that the service times are independent
Pr ( A > B + C ) = [tex]\begin {pmatrix} \dfrac{1}{3} \times \dfrac{1}{3} \times \dfrac{1}{3} \end {pmatrix}[/tex]
Pr ( A > B + C ) = [tex]\mathbf{\dfrac{1}{27}}[/tex]
