Conditional probability computation

[Nero26]

Hi all,
While solving problems related to probability I got stucked with this problem:
In some election 4 candidates A,B,C,D has the probability of being elected is 0.4,0.3,0.2,0.1 respectively.If the candidate C discard his candidateship just prior to the election ,then what will be the current probability of the remaining three?
I thought a lot but couldn't find any way to relate the probability of C with others.I sensed the probability of others will increase but I'm unable to determine it.By the way,my knowledge is limited to topics like conditional probability,Bayes' Theorem.But I can't categorize the problem in any formula.If the problem is explained please remain in the scope of my knowledge.
Or do I have to learn some new concept to solve this type of problem?
Any help will be appreciated.
Thanks.

 

[Ray Vickson]

Hi all,
While solving problems related to probability I got stucked with this problem:
In some election 4 candidates A,B,C,D has the probability of being elected is 0.4,0.3,0.2,0.1 respectively.If the candidate C discard his candidateship just prior to the election ,then what will be the current probability of the remaining three?
I thought a lot but couldn't find any way to relate the probability of C with others.I sensed the probability of others will increase but I'm unable to determine it.By the way,my knowledge is limited to topics like conditional probability,Bayes' Theorem.But I can't categorize the problem in any formula.If the problem is explained please remain in the scope of my knowledge.
Or do I have to learn some new concept to solve this type of problem?
Any help will be appreciated.
Thanks.

It is not possible to give a good, convincing answer to this question. For example, you don't know whether the supporters of C will stay home and not vote at all, or whether some of them will vote instead for A, B or D, and the proportions who do so.

I suspect that what the questioner wants you to do is look at the problem in a rather naive manner, as though the supporters of A, B, C and D were like four types of objects in a large bin (in the proportions indicated), and then get the new proportions after all the type C objects have been removed from the bin.

RGV

 

[Nero26]

It is not possible to give a good, convincing answer to this question. For example, you don't know whether the supporters of C will stay home and not vote at all, or whether some of them will vote instead for A, B or D, and the proportions who do so.

I suspect that what the questioner wants you to do is look at the problem in a rather naive manner, as though the supporters of A, B, C and D were like four types of objects in a large bin (in the proportions indicated), and then get the new proportions after all the type C objects have been removed from the bin.

RGV

Oh!you're really great.Thanks a lot.I solved it according to your instructions.Considering there were 100 voters.So when C left,20 voters left or didn't participate in election.So now among 80 voters A,B,D have 40,30,10 supporters respectively.This way their probability gets changed to 40/80,30/80,10/80 which matches the answers.
By the way,actually it is a problem in our book and I referred to its solution manual of my friend .They solved this simple problem in such a strange way that both the problem and its solution seemed very difficult to understand.Here it is:
"Solution: probability of defeat of C was =1-.2=0.8
As C left,the probability of win of each of the remaining will increase by 1/0.8=1.25 times.(Can you please say how they did it?)
So probabilities of win of A,B,D are 0.4*1.25,0.3*1.25,0.1*1.25 or 0.5,0.375,0.125 respectively."
Because of you people we can