A probability question, can anyone help me please?

[DDSelin2mori]

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Could you please help me in solving this question?

In a high school debating team consisting of 2 freshmen, 2 sophomores, 2, juniors, and 2 seniors, two students are selected to represent the school at the state debating championship. The rules stipulate that the representatives must be from different grades, but otherwise the 2 representatives are to be chosen by lottery. What is the probability tha the students selected will consist one freshman and one sophomore?


I can't understand how the answer is 1/6 but I'm getting 1/7. I'm solving this question in this way:

2 students are needed from freshman and sophomore, So there are 2 possible combination: First freshman, 2nd sophomore or first sophomore second freshman.

in first choice (First freshman, 2nd sophomore) the probability of choosing freshman is 2/8 and the sophomore is 2/7 (8-1=7 since one student is out in freshman choice) so the probability of First freshman, 2nd sophomore=(2/8)(2/7)= 1/14
The probability of first sophomore second freshman is same as 1/14. so the sum of two probabilities: (1/14)(2)= 1/7
I can't understand what is wrong in my way?

 

[mynamemule]

the probabilty of the second is 2/6. You have to eliminate the possibility of choosing the same class as you did in the first choice.

 

[Flipper405]

The thing is that the representatives must be from different grades. If you get a freshman with your first choice, you have to eliminate the other freshman from selection. The way I would think about it is: first slot must be either freshman or sophomore so it's 4/8 or 1/2. the second slot must be the other of either freshman or sophomore... 2/6 or 1/3. 1/2*1/3 = 1/6.

 

[RUmolarman]

a

 

[sacjumpman]

The thing is that the representatives must be from different grades. If you get a freshman with your first choice, you have to eliminate the other freshman from selection. The way I would think about it is: first slot must be either freshman or sophomore so it's 4/8 or 1/2. the second slot must be the other of either freshman or sophomore... 2/6 or 1/3. 1/2*1/3 = 1/6.

How come with this way, then we don't consider that there are 2 possible ways to have the outcome: freshman sophmore, or soph then freshman.

I wish I would have taken stats last quarter, maybe some practice would have helped for these ones.

 

[fireblast713]

How come with this way, then we don't consider that there are 2 possible ways to have the outcome: freshman sophmore, or soph then freshman.

I wish I would have taken stats last quarter, maybe some practice would have helped for these ones.

It's because in the question they didn't specify and order, the way it's worded it's a combination not a permutation, so order doesn't matter.

 

[DDSelin2mori]

Thank you so much for all your helps. Now I'm getting it better

 

[DDSelin2mori]

The thing is that the representatives must be from different grades. If you get a freshman with your first choice, you have to eliminate the other freshman from selection. The way I would think about it is: first slot must be either freshman or sophomore so it's 4/8 or 1/2. the second slot must be the other of either freshman or sophomore... 2/6 or 1/3. 1/2*1/3 = 1/6.

Your explanation is very helpful, thanks alot

 

[z3u2]

Could you please help me in solving this question?

In a high school debating team consisting of 2 freshmen, 2 sophomores, 2, juniors, and 2 seniors, two students are selected to represent the school at the state debating championship. The rules stipulate that the representatives must be from different grades, but otherwise the 2 representatives are to be chosen by lottery. What is the probability of the students selected will consist one freshman and one sophomore?

This is a tricky question, and the highlighted part is a phrase you need to catch when doing this kind of questions.
"The probability of the selected will consist..." means you have a new sample size. It is no longer "Select 2 students out of 8" anymore.

In simplest way, first find out what are all the possible combinations of the selected students, given the critiria above.
1. Freshman + Sophomore
2. Freshman +Junior
3. Freshman + Senior
4. Sophomore + Junior
5. Sophomore + Senior
6. Junior + Senior

The new sample size is 6 (You can find out by calculating 4 choose 2, or 4!/(2! * 2!)

Of the 6 choices, only the first one (1. Freshman + Sophomore) matches what the question is asking for.

So the answer is 1/6

you can have 100 seniors and 2 freshmen/sophomore/junior to start with, the answer will still be 1/6

 

[Streetwolf]

you can have 100 seniors and 2 freshmen/sophomore/junior to start with, the answer will still be 1/6

Actually if that were the case it would be much more likely to have a pair of kids where one of them is a senior, rather than a pair of kids where none is a senior.

 

[Flipper405]

Actually if that were the case it would be much more likely to have a pair of kids where one of them is a senior, rather than a pair of kids where none is a senior.

That's true, but if the question is interpreted the way z3u2 is, then that wouldn't matter, because only the combinations of the selections are considered. I think the wording is vague though, and would interpret it the way I think you are interpreting it