2012 Year 9 &10 Mathematics Marathon (2 Viewers)

nightweaver066

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Re: 2012 Year 9 &10 Mathematics Marathon

Here's a probability question for you guys

Bag A contains 4 green marbles and 4 red marbles. Bag B contains 3 green marbles and 1 red marble. Two marbles are drawn at random from Bag A and placed in Bag B. Two marbles are then drawn from Bag B.

Calculate the probability that two marbles drawn from Bag B are of different colours.
lol this sounds like the exact same question as the last (?) question in my school's 2U half-yearly exam.
 

iBibah

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Re: 2012 Year 9 &10 Mathematics Marathon

oh really? haha

this was from a year 10 paper at my school,
For a Year 10 paper is it quite hard, nevertheless a good question, even for 2U students.
 

ymcaec

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Re: 2012 Year 9 &10 Mathematics Marathon

Here's a probability question for you guys

Bag A contains 4 green marbles and 4 red marbles. Bag B contains 3 green marbles and 1 red marble. Two marbles are drawn at random from Bag A and placed in Bag B. Two marbles are then drawn from Bag B.

Calculate the probability that two marbles drawn from Bag B are of different colours.
Let me guess
is the answer close to 50%?
 

kev-kun

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Re: 2012 Year 9 &10 Mathematics Marathon

Here's a probability question for you guys

Bag A contains 4 green marbles and 4 red marbles. Bag B contains 3 green marbles and 1 red marble. Two marbles are drawn at random from Bag A and placed in Bag B. Two marbles are then drawn from Bag B.

Calculate the probability that two marbles drawn from Bag B are of different colours.
2 in 66 chance? (maybe?)
 

ymcaec

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Re: 2012 Year 9 &10 Mathematics Marathon

Correct! :) or more exactly,

post working?
sure

Part 1 - Picking 2 marbles from Bag A
3 possibilities - GG, GR, RR (G - green; R - red)
P(GG) =
P(GR) =
P(RR) =

Part 2 - Drawing 2 from Bag B
From Part A:
If GG is drawn - the marbles in Bag B will be GGGGGR - hence the chance drawing GR (different colour) =
If GG is drawn - the marbles in Bag B will be GGGGRR - hence the chance drawing GR =
If RR is drawn - the marbles in Bag B will be GGGGRR - hence the chance drawing GR =

Calculations
(following in form of (Part A Part B))
GG GR OR GR GR OR RR GR
 
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iBibah

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Re: 2012 Year 9 &10 Mathematics Marathon

1. If triangle PQR has side lengths 80, 60 and 40, then the shortest height is K times the longest height. Find the value of K.
2. A regular hexagon in inscribed in a circle or radius R. The length of the shortest diagonal is , find R.
Anyone want to give these a go? They are not too bad once you start.
 

iBibah

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Re: 2012 Year 9 &10 Mathematics Marathon

O_O How do you even start these type of questions lol. Hints?
Hint for No. 1: Let the longest height be x and shortest be y. Use area formula.

2. Draw it, and draw diagonals.
 

Demento1

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Re: 2012 Year 9 &10 Mathematics Marathon

sure

Part 1 - Picking 2 marbles from Bag A
3 possibilities - GG, GR, RR (G - green; R - red)
P(GG) =
P(GR) =
P(RR) =

Part 2 - Drawing 2 from Bag B
From Part A:
If GG is drawn - the marbles in Bag B will be GGGGGR - hence the chance drawing GR (different colour) =
If GG is drawn - the marbles in Bag B will be GGGGRR - hence the chance drawing GR =
If RR is drawn - the marbles in Bag B will be GGGGRR - hence the chance drawing GR =

Calculations
(following in form of (Part A Part B))
GG GR OR GR GR OR RR GR
Got the identical answer, although I had tree diagrams to solve it.
 

Demento1

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Re: 2012 Year 9 &10 Mathematics Marathon

1/2 times & R = 9 ??
The Qs are pretty poorly worded. For example, my triangle which I have drawn would say otherwise that

Probably needs to specify the 'height'.

For the diagonals, did you treat as one side of the hexagon and solve via trig?
 

iBibah

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Re: 2012 Year 9 &10 Mathematics Marathon

The Qs are pretty poorly worded. For example, my triangle which I have drawn would say otherwise that

Probably needs to specify the 'height'.

For the diagonals, did you treat as one side of the hexagon and solve via trig?
What do you understand height to mean in the area formula? Same thing here.

And for the hexagon, 9root(3) is the diagonal AC as shown in this random pic:

 
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russ3l

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Re: 2012 Year 9 &10 Mathematics Marathon

are the questions on this thread meant to be hard/challenging? I, in my whole schooling life, have never come across such convoluted questions :S (not talking about all of them...)
 

Demento1

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Re: 2012 Year 9 &10 Mathematics Marathon

What do you understand height to mean in the area formula? Same thing here.

And for the hexagon, 9root(3) is the diagonal AC as shown in this random pic:

I see... Because I drew a right angled triangle with 80 as the hypotenuse and I just simply thought of the ratio between 40 (smallest height) to 80 (largest height) - not sure if that method is correct. Could you post a solution for the 1st Q actually?

So that is what you define the 'diagonal' of the hexagon as? I'm pretty sure a diagonal of a regular hexagon is 2 times the side length of a regular hexagon (eg: line AD). I probably misunderstood what you were asking for...

are the questions on this thread meant to be hard/challenging? I, in my whole schooling life, have never come across such convoluted questions :S (not talking about all of them...)
Don't worry too much. These Qs I've found posted here, are discriminating against rote learners. A few of the Qs posted here are just time consuming and ludicrous to work out and a few are just strangely worded. So long as you have a good grasp of what the Q is asking, you shouldn't have any problems if you know what method to use to follow up. :)
 

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