Conditional probability question I believe

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Longods

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In an election for the president of the student council, it is estimated that anne has a 40% chance of winning, tanya has a 30% chance of winning, graham has a 20% chance and maria has a 10% chance. Just before the election, graham withdraws. Now what are the chances of winning for anne, tanya and maria.

Thanks for any help!
 
Suppose you took a test that had a total of 80 points.
If you scored 40 (out of 80), then what percent does that correspond to?
If you scored 30 (out of 80), then what percent does that correspond to?
If you scored 10 (out of 80), then what percent does that correspond to?
 
Jomo said:
Suppose you took a test that had a total of 80 points.
If you scored 40 (out of 80), then what percent does that correspond to?
If you scored 30 (out of 80), then what percent does that correspond to?
If you scored 10 (out of 80), then what percent does that correspond to?
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Maybe if you can point out if my logic is flawed.
Suppose you have 100 student voters; the poll shows that 40, 30, 20, 10 would vote for Anne, Tanya, Graham, and Maria, respectively (Hence the probability is given in the problem). If Graham withdraws from the race, how would the 20 people who initially would vote for Graham vote for the remaining three candidates? I believe this is the question the OP is asking.
Whereas your hint suggests that if 20 student voters are banned from voting and Graham dropped out of the race, What are the chances of winning for the remaining candidates?

However, I did arrive at the same solution. I'm wondering why that is.
 
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If a poll shows that 40, 30, 20, 10 would vote for Anne, Tanya, Graham, and Maria, respectively I would conclude that the probability of Anne winning is near 100%.
 
JayJay said:
If a poll shows that 40, 30, 20, 10 would vote for Anne, Tanya, Graham, and Maria, respectively I would conclude that the probability of Anne winning is near 100%.
Click to expand...
How did you come up with that solution?
 
The election is a one off event which the candidate with the most votes will win. The poll strongly suggests that this is Anne. This response was based on your idea of a poll (post of 5;29 am)
But your idea is flawed. The OP does not mention a poll, it gives the probability of each candidate winning (by what method, we do not know) These probabilities cannot be translated into proportions voting for each candidate.
 
JayJay said:
The election is a one off event which the candidate with the most votes will win. The poll strongly suggests that this is Anne. This response was based on your idea of a poll (post of 5;29 am)
But your idea is flawed. The OP does not mention a poll, it gives the probability of each candidate winning (by what method, we do not know) These probabilities cannot be translated into proportions voting for each candidate.
Click to expand...
The idea of the poll was to show the likelihood of how the voters are going to vote for the candidate i.e the probabilities. People can change their minds on the day of the election, so there is still uncertainty. I don't see how you can say Anna's gonna win with nearly 100% cerainty?
 
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BigBeachBanana - Sorry, I am unable to offer any more help.
Longods - To return to your original question. How will the supporters of Graham use their votes in the election?
 
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Actually I misread the problem. I thought that for example when it said Anne has a 40% chance of winning that it said that Anne had 40% of the votes.

Luckily, I think that does not change my answer. (Sorry SK).
What happens is the 20% chance that graham had gets distributed proportionally to the other candidates.

Since 125% of 80 = 100%, each remaining candidate gets an extra 25%
 
JayJay said:
If a poll shows that 40, 30, 20, 10 would vote for Anne, Tanya, Graham, and Maria, respectively I would conclude that the probability of Anne winning is near 100%.
Click to expand...
Suppose that all of graham's supporters go to anne after graham drops out. Then anne has a 60% chance of winning. How did you get a larger number than 60%?
 
You confusing the 40%, 30%, 20% and 10% probabilities (of Longods OP) with the 40%, 30%, 20% and 10% votes predicted (of Bigbeachbanana's poll)
 
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Longods said:
In an election for the president of the student council, it is estimated that anne has a 40% chance of winning, tanya has a 30% chance of winning, graham has a 20% chance and maria has a 10% chance. Just before the election, graham withdraws. Now what are the chances of winning for anne, tanya and maria.

Thanks for any help!
Click to expand...
I think Jomo's idea of prorated probabilities is the only answer that makes sense, and the most likely expected answer; but I've been struggling to find a proper justification for it. In effect, it assumes that the probability of each person winning in the event that Graham drops out is the conditional probability that they would win given that Graham doesn't win. Is there a good reason to think that would be true?

The trouble is that we aren't told on what grounds the stated probabilities were "estimated"; clearly a poll on whom individuals plan to vote for wouldn't yield probabilities at all. So we shouldn't think of the probabilities as percentages of the voters who will vote for each candidate. Perhaps they are based on probabilities of supporters of each candidate voting, or of events happening that would change people's opinions? Or are they entirely subjective?

The best we can do is to assign probabilities according to our ignorance of the underlying politics.
 
Here's how I approached the problem. Express the given probabilities as ratios in terms of Maria's.
  1. Pr(Graham wins) = 2*Pr(Maria)
  2. Pr(Tanya wins) = 3*Pr(Maria)
  3. Pr(Anne wins) = 4*Pr(Maria)
When Graham drops out, the total probability is as follow:
Pr(Maria wins) + Pr(Tanya wins) + Pr(Anne wins) = 1

Substitute the ratios:
Pr(Maria wins) + 3*Pr(Maria wins) + 4*Pr(Maria wins) = 1

Thereby, Pr(Maria wins) = 1/8 , Pr(Tanya wins)= 3/8 and Pr(Anne wins) = 4/8.

One thing that is still bugging me is that are these ratios still hold when Graham drops out?
 
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