Problem 136E
Consider the visits that result in leave without being seen (LWBS) at an emergency department in Example 28. Assume that people independently arrive for service at hospital l.
(a) What is the probability that the fifth visit is the first one to LWBS?
(b) What is the probability that either the fifth or sixth visit is the first one to LWBS?
(c) What is the probability that the first visit to LWBS is among the first four visits?
(d) What is the expected number of visits until the third LWBS occurs?
Hospital 

1 
2 
3 
4 
Total 

Total 
5292 
6991 
5640 
4329 
22,252 
LWBS 
195 
270 
246 
242 
953 
Admitted 
1277 
1558 
666 
984 
4485 
Not Admitted 
3820 
5163 
4728 
3103 
16,814 
Solution:
Step 1 of 5:
From the example 28.
Consider the visits that result in leave without being seen in an emergency department is shown in below table.


Hospital 




1 
2 
3 
4 
Total 
Total 
5292 
6991 
5640 
4329 
22,252 
LWBS 
195 
270 
246 
242 
953 
Admitted 
1277 
1558 
666 
984 
4485 
Not Admitted 
3820 
5163 
4728 
3103 
16,814 