Understanding of the probability

danique

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Understanding of the probability[solved]

I have a problem with understanding some of my statistics homework. I hope that some of you could help me understand.

In summary the question is as follows:


There are 30 people in a group, which are split up in 2 groups of 15. The first group we call group1 and the other group2. Group1 has been placed in an order from 1 till 15 and group 2 is ordered 16 till 30. In the question we need to find two persons. We do this by removing each time the 3rd person till we only have 2 people left.


So for example:

1 2 3 4 6 7 8 9 10 11.. 30; We start with number 4, first number 7 will be removed. Then number 10 will be removed. Next will be number 13. Etc, And after number 28 number 1 will be removed. till there are only have 2 people left.
The start position is random, so it could be 1 till 30.

I need to answer the following questions:


  1. What is the probability that there are 0 persons left from group1?
  2. What is the probability that there is 1 person left from group1?
  3. What is the probability that the two persons, who are still there are both from group1?
Someone told me the answers, but I do not understand them. So I hope that someone could explain it to me. I got the following answers:
1) 4/30
2) 22/30
3) 4/30

I also asked the question at
stackexchange. This was the answer: http://math.stackexchange.com/questions/1266973/understanding-of-the-probability
 
Last edited:
I have a problem with understanding some of my statistics homework. I hope that some of you could help me understand.

In summary the question is as follows:


There are 30 people in a group, which are split up in 2 groups of 15. The first group we call group1 and the other group2. Group1 has been placed in an order from 1 till 15 and group 2 is ordered 16 till 30. In the question we need to find two persons. We do this by removing each time the 3rd person till we only have 2 people left.


So for example:

1 2 3 4 6 7 8 9 10 11.. 30; We start with number 4, first number 7 will be removed. Then number 10 will be removed. Next will be number 13. Etc, And after number 28 number 1 will be removed. till there are only have 2 people left.
The start position is random, so it could be 1 till 30.

I need to answer the following questions:


  1. What is the probability that there are 0 persons left from group1?
  2. What is the probability that there is 1 person left from group1?
  3. What is the probability that the two persons, who are still there are both from group1?
Someone told me the answers, but I do not understand them. So I hope that someone could explain it to me. I got the following answers:
1) 4/30
2) 22/30
3) 4/30

I also asked the question at
stackexchange. This was the answer: http://math.stackexchange.com/questions/1266973/understanding-of-the-probability
Interesting problem. You really are supposed to show us your work. Since this is a bit (just a bit) hard I will give you a hint. Call a pattern the order the numbers are removed. How many different patterns are there?? Start by removing 1 1st, then start over again by removing 2 1st, etc. Again, how many different patterns are there. Once you have the different patterns the problem should be simple. If you still need help then show us the work you have done so far. Another hint is that 3 divides 30.
 
Interesting problem. You really are supposed to show us your work. Since this is a bit (just a bit) hard I will give you a hint. Call a pattern the order the numbers are removed. How many different patterns are there?? Start by removing 1 1st, then start over again by removing 2 1st, etc. Again, how many different patterns are there. Once you have the different patterns the problem should be simple. If you still need help then show us the work you have done so far. Another hint is that 3 divides 30.


Thank you for the hint. I got the solution:)
 
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Thank you for the hint. I got the solution:)
So what results did you get? I realized that the best way to do this, if not the only way, was to find out how far apart the two people are who are left. The rest is easy from there. The answers you were told are not correct.
 
Sure.

I started to look for a pattern. So first I started deleting person 1 and 4, Till I only had 2 person left. I did this in excel, but I deleted it. But I think this gave me person 17 and person 27.
Next I did another try, but now I started with deleting person 2, till I only had 2 people left. This gave me person 18 and 28.

So lets say p1 & p2 are the persons that are left. I know now that if p1=1, than p2=10. Now I can calculate the probability.

So for 0 people from group1. p1 can between 15 and 20. This was my first answer: 5 out of 30

For 1 people from group1, I did 1-5/30-5/30=1-10/30=20/30.

For 2 people from group1. I can look at the answer of 0 people from group1, because both groups had the same amount of persons. This is also 5/30.
 
Sure.

I started to look for a pattern. So first I started deleting person 1 and 4, Till I only had 2 person left. I did this in excel, but I deleted it. But I think this gave me person 17 and person 27.
Next I did another try, but now I started with deleting person 2, till I only had 2 people left. This gave me person 18 and 28.

So lets say p1 & p2 are the persons that are left. I know now that if p1=1, than p2=10. Now I can calculate the probability.

So for 0 people from group1. p1 can between 15 and 20. This was my first answer: 5 out of 30

For 1 people from group1, I did 1-5/30-5/30=1-10/30=20/30.

For 2 people from group1. I can look at the answer of 0 people from group1, because both groups had the same amount of persons. This is also 5/30.
I did not get 17 and 30 when I deleted 1 first. Redo that.

Lets work with your (incorrect) numbers. you were 1st left with 17 and 27. These numbers are 10 apart. That is all you need to easily proceed. You will have:
17 27, 18 28, 19 29, 20 30, 21 1, 22 2,...30 10, 1 11, 2 12,...16 26.

Now just count how many have 0 in group 1, 1 in group 1 and 2 in group 1
 
I did not get 17 and 30 when I deleted 1 first. Redo that.

Lets work with your (incorrect) numbers. you were 1st left with 17 and 27. These numbers are 10 apart. That is all you need to easily proceed. You will have:
17 27, 18 28, 19 29, 20 30, 21 1, 22 2,...30 10, 1 11, 2 12,...16 26.

Now just count how many have 0 in group 1, 1 in group 1 and 2 in group 1


thank you for the feedback, but I am not sure if you understand my solution. I did not get 27 and 30 when I deleted 1 first. I had 17 and 27.
I did this several times and everytime I got 17 and 27. This is how I looked for the pattern:
Probability pattern.jpg

I also think I did this the same as you described, and this gave me the previous answers.

1) 5/30
2) 20/30
3) 5/30

Is possible that you show me your answers?
 
thank you for the feedback, but I am not sure if you understand my solution. I did not get 27 and 30 when I deleted 1 first. I had 17 and 27.
I did this several times and everytime I got 17 and 27. This is how I looked for the pattern:
View attachment 5293

I also think I did this the same as you described, and this gave me the previous answers.

1) 5/30
2) 20/30
3) 5/30

Is possible that you show me your answers?
Why do you think that I got 27 and 30 left initially? I actually never said that.
I will try to write out what I got.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30

3 5 8 9 12 14 17 18 21 23 26 27 30

3 8 9 14 17 21 23 27 30

8 9 17 21 27 30

9 17 27 30

17 27

I too did this a few times and always had 17 and 30 left. Oh well, I was wrong and you were correct. Good for you!
 
Why do you think that I got 27 and 30 left initially? I actually never said that.
I will try to write out what I got.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30

3 5 8 9 12 14 17 18 21 23 26 27 30

3 8 9 14 17 21 23 27 30

8 9 17 21 27 30

9 17 27 30

17 27

I too did this a few times and always had 17 and 30 left. Oh well, I was wrong and you were correct. Good for you!

I really have appreciated your help, thx:)
 
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