# number of supporters?

#### jorald745

##### New member
A.

In a large city the number of supporters for the mayor is not known.

If two citizens are chosen at random, the probability of choosing one supporter and another one that opposes the incumbent mayor is 0.18.

It is known that the number of supporters for the incumbent mayor exceeds that of his opponents.

-1 Why is it important to say that the city is large?
-2 What is the proportion of supporters for the incumbent mayor?

B.

In a big city there are residents who support the incumbent mayor and others who oppose him.

If three people are randomly selected from the city, the probability of not more than two supporting the incumbent mayor is 0.992.

- What is the proportion of supporters for the incumbent mayor?

#### Subhotosh Khan

##### Super Moderator
Staff member
A.

In a large city the number of supporters for the mayor is not known.

If two citizens are chosen at random, the probability of choosing one supporter and another one that opposes the incumbent mayor is 0.18.

It is known that the number of supporters for the incumbent mayor exceeds that of his opponents.

-1 Why is it important to say that the city is large?
-2 What is the proportion of supporters for the incumbent mayor?

B.

In a big city there are residents who support the incumbent mayor and others who oppose him.

If three people are randomly selected from the city, the probability of not more than two supporting the incumbent mayor is 0.992.

- What is the proportion of supporters for the incumbent mayor?
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#### jorald745

##### New member
Please follow the rules of posting in this forum, as enunciated at:

the thing is that I don't even know where to start...

#### Jomo

##### Elite Member
Can you at describe what equals 0.18? How about what is meant by it is known that the number of supporters for the incumbent mayor exceeds that of his opponents?

#### tkhunny

##### Moderator
Staff member
the thing is that I don't even know where to start...
We hear that a lot. It is almost never true.

A.1 You must know something about large populations vs small populations unless you have never attended class and also failed to read any pertinent materials.
A.2 Ponder $$\displaystyle (p+q)^{2}$$. I suspect you already know how to do this. What does it mean? How does it relate to the question? That's up to you.

B.1 "more than 2" is EXACTLY the same as "3".
B.2 Almost the same as A.2.

#### jorald745

##### New member
We hear that a lot. It is almost never true.

A.1 You must know something about large populations vs small populations unless you have never attended class and also failed to read any pertinent materials.
A.2 Ponder $$\displaystyle (p+q)^{2}$$. I suspect you already know how to do this. What does it mean? How does it relate to the question? That's up to you.

B.1 "more than 2" is EXACTLY the same as "3".
B.2 Almost the same as A.2.
A.1. I don't know, we actually didn't learn it. We have quarantine because of the coronavirus and our teacher gave us this task to do, and we didn't learn it before, I don't know how we're supposed to do it...

A.2,B.1.,B.2. alright I'll try

#### jorald745

##### New member
Can you at describe what equals 0.18? How about what is meant by it is known that the number of supporters for the incumbent mayor exceeds that of his opponents?
well, I guess that the probability to choose a supporter and someone else who's opposed, is 0.18. I guess that we can infer that the possibility to choose a supporter is greater than 0.9 and smaller than 0.18 because there are more supporters than opponents. I might be really off though because I don't see how this helps

#### Jomo

##### Elite Member
well, I guess that the probability to choose a supporter and someone else who's opposed, is 0.18. I guess that we can infer that the possibility to choose a supporter is greater than 0.9 and smaller than 0.18 because there are more supporters than opponents. I might be really off though because I don't see how this helps
It doesn't matter if it helps or not you should know what it means.
If two citizens are chosen at random, the probability of choosing one supporter and another one that opposes the incumbent mayor is 0.18
The wording might not be the best but here is what I think it means. You ask two random people whether they support or not support the incumbent mayor. The probability that you get one person says support and the other person says does not support the incumbent mayor is 0.18

You never responded to my other question. What is meant by it is known that the number of supporters for the incumbent mayor exceeds that of his opponents?

You can't do the problems if you do not know what is being said.

What is being said does not require you to know probability beyond what you have been taught in class already. Maybe what to do with the probabilities might be new to you but where are not up to that part yet. Please answer my remaining question.

#### tkhunny

##### Moderator
Staff member
A.1. I don't know, we actually didn't learn it. We have quarantine because of the coronavirus and our teacher gave us this task to do, and we didn't learn it before, I don't know how we're supposed to do it...

A.2,B.1.,B.2. alright I'll try

A.2
I'll use the notation "P(result)" to mean "the probability that the result will be observed". Don't confuse this "P" with the following definition.
p = portion of the large population that favors the mayor
q = 1-p = portion of the large population that does not favor the mayor
We're assuming there are only two opinions, I guess.
(p+q)^2 = p^2 + 2pq + q^2 = P(two who favor the mayor) + P(one of each) + P(two who don't favor the mayor)
Problem states: 2pq = 0.18 <== It is important to see this.
Algebra: pq = 0.09
Substitution: p(1-p) = 0.09
Can you find p?

A.1
What if the town has only 5 people? The ONLY possibilities for % that favor the mayor are 0, 20, 40, 60, 80, 100.
0 * 1 = 0
.2 * .8 = 0.16
.4 * .6 = 0.24
Pretty tough to get 2pq = 0.18 out of that.
The more people we get, the closer we are to an essentially continuous distribution and we have a chance to solve for the desired values.
Can you think of a reason for a larger population that is not related merely to the calculation method?

Let's see if you can extend this to B.