Question

Ambulance response time.Geographical Analysis(Jan. 2010) presented a study of emergency medical service (EMS) ability to meet the demand for an ambulance. In one example, the researchers presented the following scenario. An ambulance station has one vehicle and two demand locations, A and B. The probability that the ambulance can travel to a location in under 8 minutes is .58 for location A and .42 for location B. The probability that the ambulance is busy at any point in time is .3.

a.Find the probability that EMS can meet the demand for an ambulance at location A.

b.Find the probability that EMS can meet the demand for an ambulance at location B.

Short answer

1. 0.406
2. 0.294

Step-by-step solution

 Step 1: Given

Let P (Busy) be the probability that the ambulance is busy.

Therefore, let P (Free) be the probability that the ambulance is free

P (A) is the probability that the ambulance reaches location A on time

P (B) is the probability that the ambulance reaches location B on time

Finding the probability that EMS can meet the demand for an ambulance at location A.

The probability of the ambulance reaching location A on time is dependent on whether it is free and the time.

$\begin{array}{c}\text{P}\left(\text{A}\right)\text{=P}\left(\text{A|Free}\right)\text{×P}\left(\text{Free}\right)\\ \text{=0.58×0.7}\\ \text{=0.406}\end{array}$

Therefore, P(A) = 0.406.

Finding the probability that EMS can meet the demand for an ambulance at location B.

Following the same logic as above,

$\begin{array}{c}\text{P}\left(\text{B}\right)\text{=P}\left(\text{B|Free}\right)\text{×P}\left(\text{Free}\right)\\ \text{=0.42×0.7}\\ \text{=0.294}\end{array}$

Therefore, the probability that the ambulance reaches location B on time is 0.294.