Wenona
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 Original Post 2011-Sep-11, 02:05 PM
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My daughter is in grade 8 and is doing some probability in maths.
She asked for some help with an assignment that included some questions about a raffle.
The raffle has 36 tickets that cost 80 cents each. The person running the raffle wants to make a profit of $22.
They had to first workout what the total revenue from the raffle was ie $28.80
Then what the prize needed to be for the promoter to make their profit ie $6.80
They then had to do up a table showing the probability of winning if buying 1 to 10 tickets, the cost of the tickets and the profit you would make if you bought those tickets and won, ie
1 ticket - cost 80c - 1/36 chance of winning - profit $$6.00
2 tickets - $1.60 - 1/18 - $5.20
3 tickets - $2.40 - 1/12 - $4.40
4 tickets - $3.20 - 1/9 - $3.60
5 tickets - $4.00 - 5/36 - $2.80
6 ticket - $4.80 - 1/6 - $2.00
7 tickets - $5.60 - 7/36 - $1.20
8 tickets - $6.40 - 2/9 - $0.40
9 tickets - $7.20 - 1/4 - loss 0.40c
10 tickets - $8.00 - 5/18 - loss $1.20
So far so good.
The next question was, how many tickets should you buy and why?
My daughter told me she didn't need help with this bit because they had discussed it in class.
Good I said, can you tell me why the amswer is zero?.
What? She gives me a funny look and tells me the answers not zero it's 6.
What!!!!!!!!!!!!!
How can it possibly be 6 I ask.
The teacher said that you shouldn't buy 9 or 10 because you still lose if your ticket comes out, and 1 or 2 doesn't give you enough chance of winning. 6 is right because it gives you a good chance of winning a good amount.
A brief summary of my response is it included some not very complimentary comments about the education system, a discussion of negative expectation and rational behaviour and me fronting the teacher on Monday morning for an explanation.
My daughter is of course horrified at the thought of me contacting her teacher. I've met the teacher at parent-teacher interview night and he seems a nice enough fellow, my daughter really likes him and we actually give him credit for her getting her first ever A in maths. My partner says I should let it go, it's not that important and it's not worth causing my daughter grief or embarrassment at school. I'm still dumbfounded and a bit outraged.
So, what do you reckon? Do I make a case of it or not?
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Authorized
Steward
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2011-Sep-11, 02:13 PM
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No need to make a case of it. Just bring it up politely at the next Parent teacher night or if you bump into him when picking your daughter up.
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el zoro
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2011-Sep-11, 02:15 PM
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I'd just make sure you ring him when you want to sell some raffle tickets.
He'll be good for 6. 
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arakaan
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2011-Sep-11, 02:25 PM
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Does your daughter understand why your saying zero? If she does then that's her answer and she explains why on the assignment as per the question asked.
If the teacher then marks it wrong on the assignment well then you have talking point.
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Steward
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2011-Sep-11, 02:29 PM
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Why is it ZERO ?
Is it zero in a capitalist world and 6 in a socialist world ?
Although I would have thought it would be 1 in a socialist setting as than all 36 buyers have an equal chance ?
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JWesleyHarding
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2011-Sep-11, 02:34 PM
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What should you do?
With a rake like that you should tell P1 and P2 you've found out where EFK is.
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PoisonPen7
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2011-Sep-11, 03:11 PM
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I think the question should have been: - If you are committed to buying raffle tickets, what would be......... And I would have thought the answer would be 1, probably for the same reasons the correct answer without the commitment is 0.  |
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Thesmartman
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2011-Sep-11, 03:33 PM
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Then what the prize needed to be for the promoter to make their profit ie $6.80
Mate,
Is this sentence correct before I finalise my thinking?
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JWesleyHarding
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2011-Sep-11, 04:56 PM
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Then what the prize needed to be for the promoter to make their profit ie $6.80
Mate,
Is this sentence correct before I finalise my thinking?
Yes, that threw me for a moment. The ie threw me. The ie was meant for the "prize" not the "profit". |
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Thesmartman
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2011-Sep-11, 06:09 PM
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I assume that is correct also so this is my response.
Probability, this is what we are discussing. There is a good saying, "do not get your probabilities mixed up with your possibilities". Very true at times.
The scenario which is painted is based on profit and then how many tickets people would buy given the prize is not lucrative. We are also looking at it from what the expectations of profit would be for a person aged approximately 13yrs of age.
Firstly, there is no incorrect answer, there will be better answers or moreover more correct answers.
One would assume that 8 or 9 are not what we would hope to see as the common response for a person of this age. However, zero is certainly not a more appropriate response either.
This is because the scenario accepts we are selling to tickets and that people "will" purchase a ticket. (at least 1 ticket) I would also submit that 6 is not the response either if I was looking for an answer to the probability of this scenario if I was the teacher.
My final response would fair to assess that most people pursue value for money and likelihood of winning most likely would purchase 3 - 4 tickets. I would clarify in my response that this range is probably going to produce the best possibility of drawing the winning ticket without over purchasing.
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In relation to approaching the teacher, I would ask my daughter if she felt comfortable with discussing it with the teacher and preferably in an open forum within the class room given this a likely opportunity.
Maybe you could draft her question for her as something like, "I was discussing my home work with the father and his opinion was (x) based on (y).
If this would never eventuate then unless I was truly not satisfied that this bloke is a good teacher, I would most likely go about it at the parent teacher night, or via the principal or head of maths.
But a difficult call based on what your daughter really wants versus the challenges of being a good parent.
i think what is great about your question is that you are a "hands on" parent mate. Congrats and best of luck.
Thesmartman
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JWesleyHarding
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2011-Sep-11, 06:23 PM
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The teacher has obviously stuffed up the question.
I'd just drop him a note telling him that I have a career path mapped out for my daughter as a professional punter and as such I don't want him filling her head with notions of betting into a pool with that rake %.
If he's the good bloke you believe he is he'd take that as intended.
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Wenona
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2011-Sep-11, 06:45 PM
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The question was : what the prize needed to be for the promoter to make their profit.
i.e. is the answer, $6.80.
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Wenona
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2011-Sep-11, 06:46 PM
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I think the question should have been: - If you are committed to buying raffle tickets, what would be......... And I would have thought the answer would be 1, probably for the same reasons the correct answer without the commitment is 0. I agree, and I went through that with her. |
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Wenona
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2011-Sep-11, 06:58 PM
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I assume that is correct also so this is my response.
Probability, this is what we are discussing. There is a good saying, "do not get your probabilities mixed up with your possibilities". Very true at times.
The scenario which is painted is based on profit and then how many tickets people would buy given the prize is not lucrative. We are also looking at it from what the expectations of profit would be for a person aged approximately 13yrs of age.
Firstly, there is no incorrect answer, there will be better answers or moreover more correct answers.
One would assume that 8 or 9 are not what we would hope to see as the common response for a person of this age. However, zero is certainly not a more appropriate response either.
This is because the scenario accepts we are selling to tickets and that people "will" purchase a ticket. (at least 1 ticket) I would also submit that 6 is not the response either if I was looking for an answer to the probability of this scenario if I was the teacher.
My final response would fair to assess that most people pursue value for money and likelihood of winning most likely would purchase 3 - 4 tickets. I would clarify in my response that this range is probably going to produce the best possibility of drawing the winning ticket without over purchasing.
-----------------------
In relation to approaching the teacher, I would ask my daughter if she felt comfortable with discussing it with the teacher and preferably in an open forum within the class room given this a likely opportunity.
Maybe you could draft her question for her as something like, "I was discussing my home work with the father and his opinion was (x) based on (y).
If this would never eventuate then unless I was truly not satisfied that this bloke is a good teacher, I would most likely go about it at the parent teacher night, or via the principal or head of maths.
But a difficult call based on what your daughter really wants versus the challenges of being a good parent.
i think what is great about your question is that you are a "hands on" parent mate. Congrats and best of luck.
Thesmartman
I'm OK with a grade 8 question of this sort not attempting to deal with the concept of Utility. However I would argue that such a question even at grade 8 level should deal with positive or negative expectation. I think doing so would lead to the class to a far better understanding. The think one of the things that really made me confused is how a teacher could argue that 6 tickets is better than 4 or 3 etc. |
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winner
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2011-Sep-11, 07:18 PM
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So, what do you reckon? Do I make a case of it or not?
Do you check your daughter's homework regularly? Does the teacher have a history of errors? |
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