Question

If the arrival and departure rates in a public telephone booth with a single phone are 1/12 and 1/4 respectively. What is the probability that the phone remains busy?

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{1}{3}$

$\text{P(Phone is busy ) = 1 - P (No customer in the booth)}$

$=1-(1-\frac{\lambda }{\mu })=\frac{\lambda }{\mu }=\frac{1}{12}/\frac{1}{4}=\frac{1}{3}$