Bob is facing a dilemma. His mother is on the waiting listfor a kidney transplan
ID: 2953406 • Letter: B
Question
Bob is facing a dilemma. His mother is on the waiting listfor a kidney transplant, and she knows she is the first person onthe list - so her mother will be called whenever a kidney becomesavailable, in which case she must go under surgery for transplantimmediately since kidneys perish very quickly.Bob needs to go on anoverseas trip, but is afraid the hospital may call his mother forthe transplant operation while he's gone.So, he is thinking ofcutting her trip length from 20 days to 10 days. Will that decisionmake it less likely that he is absent if his mother is called? Ifso, how much less likely? Note that there are no further datafor this problem, so do the best you can given the lack ofinformation.State and justify any assumptions you make.Explanation / Answer
Since availability of Kidney can be thought of like occurring ofan event with in a time frame. So this follows poissondistribution.
Lets say kidneys available at an average rate of forevery 10 days.
So P(Bob will be absent if he takes 10 day trip)=P(at leastkidney get available in first 10 days)
= 1=P(no kidney is available in 10 days)
=1-(t)-k * e(-t) /k!
=1- (*1)-0 * e(-*1) /0! = 1- e-
P(Bob will be absent if he takes 20 day trip)=P(at least kidneyget available in first 20 days)
= 1=P(no kidney is available in 20 days)
=1-(t)-k * e(-t) /k!
=1- (*2)-0 * e(-*2) /0! = 1- e-2
Since 1- e- < 1- e-2 cutting his trip short will lessen the likeliness that hewill be absent for the operation
Hope it is helpful. Feel free to ask for any clarifications