Answer:
A) 0
B) 1/27
C) 1/4
Step-by-step explanation:
Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. The formular is represented below:
P(A) = Number of Favorable Outcomes / Total Number of Possible Outcomes
Let S1, S2, S3 represent the service times for A , B and C respectively
a) PS1 > S2 + S3 =0
Thus there is no probability that A is still in the office after the other two have left. The probability is 0.
b) Let
θ
θ be the possible values S1, S2 , S3 then
S1 > S2 + S3
⇔
⇔ S1 = 3 , S2 = 1 , S3 = 1
P( S1 > S2 + S3 ) = P(S1=3)P(S2=1)P(S3=1)
⇔
⇔ 1/3 x 1/3 x 1/3 = 1/27
(c) P(X >Y) = 1/2 where X,Y belongs { A, B , C}
where A,B,C represents the waiting times of clients A,B,C respectively. Now due to the memoryless property of exponential distribution. we have that
P(A>B+C)
=P(A>B+C/A>B)P(A>B)
=P(A>C)P(A>B)
=1/2X1/2
=1/4
