Exam 1 Solutions
ISYE6644 – Spring 2026
TA: Brian Kearney
Slides and Solutions from ISYE6644 Course materials and Solution sets
,Question 1
TRUE or FALSE? In a single-server queue simulation, if the arrival rate of customers
showing up is less than the service rate of the single-server, then the queue will not
explode to infinity.
,Question 1
TRUE or FALSE? In a single-server queue simulation, if the arrival rate of customers
showing up is less than the service rate of the single-server, then the queue will not
explode to infinity.
Solution: If the arrival rate is less than the service rate the queue will get cleaned
out eventually.
So, the answer is TRUE. □
, Question 2
Consider a family that has 2 children. Assume that P(kid is a boy) = 1Τ3 and
P(kid is a girl) = 2Τ3, and that the genders of the 2 kids are independent. What is the
probability that both kids are girls given that we know at least 1 of them is a girl?
(a) 1/16
(b) 1/8
(c) 1/5
(d) 1/4
(e) 1/2
ISYE6644 – Spring 2026
TA: Brian Kearney
Slides and Solutions from ISYE6644 Course materials and Solution sets
,Question 1
TRUE or FALSE? In a single-server queue simulation, if the arrival rate of customers
showing up is less than the service rate of the single-server, then the queue will not
explode to infinity.
,Question 1
TRUE or FALSE? In a single-server queue simulation, if the arrival rate of customers
showing up is less than the service rate of the single-server, then the queue will not
explode to infinity.
Solution: If the arrival rate is less than the service rate the queue will get cleaned
out eventually.
So, the answer is TRUE. □
, Question 2
Consider a family that has 2 children. Assume that P(kid is a boy) = 1Τ3 and
P(kid is a girl) = 2Τ3, and that the genders of the 2 kids are independent. What is the
probability that both kids are girls given that we know at least 1 of them is a girl?
(a) 1/16
(b) 1/8
(c) 1/5
(d) 1/4
(e) 1/2
