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Grade 9 Maths Question (Not for the faint-hearted)

This question was originally posted in the “Grade 9 Maths Paper...” thread but thought I’d create its own thread to raise awareness.
@Notnek and I wrote this:

Cheryl has a bag of cyan and turquoise coloured discs.
The ratio of cyan discs to the ratio of turquoise discs is 3:1.
The probability of Cheryl removing 2 of the same coloured discs, and then 1 of the opposing coloured discs is 1/5.

(a) Determine how many cyan discs were originally in the bag.

(b) The discs in the bag are all similar cylinders with equal density. The radii of cyan discs and turquoise discs are in the ratio 1:2.

Cheryl takes all of the discs out of the bag and stacks them on top of each other (circular face touching circular face) on the ground to form a tower of discs with a turquoise disc at the bottom of the tower. It is only known that there is a turquoise at the bottom of the tower.
Cheryl then chooses a disc at random from the tower and removes it so that a smaller tower is formed. Each disc has an equal chance of being selected.

Find the probability that the change in the pressure exerted by the tower on the ground is greater than 20%.
You must show all your working. (You can assume that the force exerted by an object on the ground is proportional to its mass).

Answers/attempts in spoilers please :smile:

(edited 6 years ago)

Reply 1

DrSebWilkes

I always find stats questions harder than they are, so here is one to keep my stats understanding up. Or at least me trying!!

Spoiler

(edited 6 years ago)

Reply 2

Y2_UniMaths

Original post by DrSebWilkes

I always find stats questions harder than they are, so here is one to keep my stats understanding up. Or at least me trying!!

Spoiler

Reply 3

DrSebWilkes

Original post by Y11_Maths

Spoiler

BEATEN AGAIN BY NOT FULLY READING THE QUESTION WOOOOOOOOOOOOW

*goes crazy*

Spoiler

Reply 4

Y2_UniMaths

Original post by DrSebWilkes

BEATEN AGAIN BY NOT FULLY READING THE QUESTION WOOOOOOOOOOOOW

*goes crazy*

Spoiler

Haha don’t worry I do this all the time and drop marks coz I forget I haven’t finished.

Spoiler

Reply 5

DrSebWilkes

Original post by Y11_Maths

Haha don’t worry I do this all the time and drop marks coz I forget I haven’t finished.

Spoiler

I'll have a look before bed

I'm procrastinating way too much from my actual Stats homework hahah

Cheers for this though was fun

Reply 6

Y2_UniMaths

Original post by DrSebWilkes

I'll have a look before bed

I'm procrastinating way too much from my actual Stats homework hahah

Cheers for this though was fun

Your welcome :smile:

Reply 7

ghostwalker

Original post by Y11_Maths

Cheryl takes all of the discs out of the bag and stacks them on top of each other (circular face touching circular face) on the ground to form a tower of discs with a turquoise disc at the bottom of the tower. It is only known that there is a turquoise at the bottom of the tower.
Cheryl then chooses a disc at random from the tower and removes it so that a smaller tower is formed. Each disc has an equal chance of being selected.

Presumably the discs are stacked at random and when a disc is removed, then so are all the discs above it??

Reply 8

Y2_UniMaths

Original post by ghostwalker

Presumably the discs are stacked at random and when a disc is removed, then so are all the discs above it??

I don’t know what you mean by “then so are all the discs above it” but yes the discs are stacked at random and only one is removed from the tower, all the others remain.

Reply 9

ghostwalker

Original post by Y11_Maths

I don’t know what you mean by “then so are all the discs above it” but yes the discs are stacked at random and only one is removed from the tower, all the others remain.

I have a suspicion there's a glitch in the question then. I'll await developments.

Reply 10

Y2_UniMaths

Original post by ghostwalker

I have a suspicion there's a glitch in the question then. I'll await developments.

There is no glitch? What’s wrong?

Reply 11

ghostwalker

Original post by Y11_Maths

There is no glitch? What’s wrong?

Depends what you're expecting the answer to the last part to be. As I said, "I'll await developments".

Original post by Y11_Maths

@Notnek

Original post by ghostwalker

Depends what you're expecting the answer to the last part to be. As I said, "I'll await developments".

I think it's okay but I wouldn't be that surprised if there was some glitch in the wording or solution for b). I got it wrong the first time and I made it up!

Reply 14

Y2_UniMaths

Original post by Notnek

I think it's okay but I wouldn't be that surprised if there was some glitch in the wording or solution for b). I got it wrong the first time and I made it up!

Is there any specific part in the wording of the question you would change/rewrite so I can edit it in the post?

Reply 15

Notnek

Original post by Y11_Maths

Is there any specific part in the wording of the question you would change/rewrite so I can edit it in the post?

Possibly but it's too wordy as it is plus the thing I was considering would probably make the question sound more confusing than it is. I'd say leave it for now and await developments :smile:

Reply 16

Y2_UniMaths

Original post by Notnek

Possibly but it's too wordy as it is plus the thing I was considering would probably make the question sound more confusing than it is. I'd say leave it for now and await developments :smile:

Yes sir