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# How would you explain this? watch

1. There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow. Hannah takes at random a sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag.she eats the sweets. The probability that Hannah eats 2 orange sweets is 1/3. Show that n^2-n-90=0
2. The BBC made a video explaining the infamous Hannah's sweets question:
https://youtu.be/N980VBpu3OE
3. (Original post by Jenella)
There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow. Hannah takes at random a sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag.she eats the sweets. The probability that Hannah eats 2 orange sweets is 1/3. Show that n^2-n-90=0

As a hint, draw a tree diagram for the two picks and write down the probabilities in terms of n
4. (Original post by Jenella)
There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow. Hannah takes at random a sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag.she eats the sweets. The probability that Hannah eats 2 orange sweets is 1/3. Show that n^2-n-90=0
6 Sweets orange, rest yellow.
First take from bag=6/n chance it will be orange.
As only 5 left, you 5/(n-1), as you have taken an orange sweet already, 6-1=5, you have also taken a sweet from the total, so its n-1. Basic probability means the chance of getting 2 orange sweets in a row is the first probability multiplied by the second one(for instance if the probability of getting something is half, getting it twice is 1/4, because 1/2 x 1/2=1/4)

So now you can go to- 6/n x 5/(n-1)=30n^2-n
1/3=30n^2-n
Equalize your denominators, so 30/90=30n^2-n n^2-n=90 Done.
Not as difficult as it looks, but takes a while to think about it. Surprised it was in an exam paper, this is a more Maths Challenge question.
5. (Original post by Zoqua)
6 Sweets orange, rest yellow.
First take from bag=6/n chance it will be orange.
As only 5 left, you 5/(n-1), as you have taken an orange sweet already, 6-1=5, you have also taken a sweet from the total, so its n-1. Basic probability means the chance of getting 2 orange sweets in a row is the first probability multiplied by the second one(for instance if the probability of getting something is half, getting it twice is 1/4, because 1/2 x 1/2=1/4)

So now you can go to- 6/n x 5/(n-1)=30n^2-n
1/3=30n^2-n
Equalize your denominators, so 30/90=30n^2-n n^2-n=90 Done.
Not as difficult as it looks, but takes a while to think about it. Surprised it was in an exam paper, this is a more Maths Challenge question.
No, it's actually quite basic to be a Maths challenge problem. This type of question now is in the grade 7-9 new spec. To be fair, I don't understand why it received that attention as I don't think it does take a while to think about; it's standard tree diagrams that had been taught (or even without tree diagrams).
6. (Original post by thekidwhogames)
No, it's actually quite basic to be a Maths challenge problem. This type of question now is in the grade 7-9 new spec. To be fair, I don't understand why it received that attention as I don't think it does take a while to think about; it's standard tree diagrams that had been taught (or even without tree diagrams).
I know it's going to be basic by the time I do the exam, I'm only in Year 10, so if I can solve it why can't Year 11's? I wasn't saying it was difficult, I was saying it was a slightly more creative problem, that could be in the Maths Challenge(although I agree it would only be in the first easy 15 questions). New 7-9 spec isn't as hard as everyone says it is, and I agree with you that it's not that special as a problem.
7. (Original post by Zoqua)
I know it's going to be basic by the time I do the exam, I'm only in Year 10, so if I can solve it why can't Year 11's? I wasn't saying it was difficult, I was saying it was a slightly more creative problem, that could be in the Maths Challenge(although I agree it would only be in the first easy 15 questions). New 7-9 spec isn't as hard as everyone says it is, and I agree with you that it's not that special as a problem.
I agree with that. Yeah, the 7-9 isn't as hard as everyone says it is (I've already sat it; first cohort). Good luck with Maths GCSE. Will you be taking FM GCSE + FMSQ next year?
8. (Original post by thekidwhogames)
I agree with that. Yeah, the 7-9 isn't as hard as everyone says it is (I've already sat it; first cohort). Good luck with Maths GCSE. Will you be taking FM GCSE + FMSQ next year?
Yes, I will take the AddMaths classes for Further Maths, and I intend to do Double Maths(Maths and Further Maths) at A Level, and probably at University as well, Maths is the subject in my family, thanks by the way

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