Do my Penguin for me

[conzer16]

Thanks Letty

 

You have been most helpful to me recently

[MasterYoda]

I don't think it's j'etait. J'etais is l'imprefait, and j'ai ete is passe compose.

[Demuwan]

Statistics Ques

 

Each of the 6 cards has a different single letter on it. The letters are A B C D E and F. The cards are shuffled and then placed in a row.

 

(iii) The cards are now shuffled and placed face down. Three of the cards are selected at random. Find the Probablity that at least 1 of the cards selected is a vowel.

 

?

[Ellmeister]

This seems to quick an answer to have reached and considering I haven't done statistics yet, I think its 1/3 :S because you have a 2/6 chance.. oh wait now that I think about it, don't you have to draw that tree thing for all possibilities or something?

 

Still going with 1/3

[Demuwan]

This seems to quick an answer to have reached and considering I haven't done statistics yet, I think its 1/3 :S because you have a 2/6 chance.. oh wait now that I think about it, don't you have to draw that tree thing for all possibilities or something?

 

Still going with 1/3

 

 

Might be wrong but I don't think so. As you have a 1/3 chance of picking a vowel if you pick one card however you then have to pick 3 which means that if you didn't pick a vowel first time, you have 5 cards left with 2 vowels left and if you don't pick a vowel again you have 4 cards left and 2 vowels.

 

I have a few answers but as my teacher forgot to give me a marksheme I don't know which one is right.

[Zell]

The probability of any one combination is going to be:

 

1/6 x 1/5 x 1/4 = 1/120

 

So we need to find how many of those cominations have at least one vowel.

 

Let's say our first card was a vowel. Any combination of 2nd and 3rd card would have "at least one vowel". The number of these combinations would be 2 x 5 x 4 = 20.

 

If our first card was not a vowel, but our second card was a vowel, then any combination of 3rd card would have "at least one vowel". The number of these combinations would be 4 x 2 x 4 = 32.

 

If our first and second cards were not vowels, there would still be 2 vowels left. So the number of combinations would be 4 x 3 x 2 = 24.

 

20 + 32 + 24 = 96

 

Therefore there are 96 combinations out of a possible 120.

 

Therefore p(at least one vowel) = 96/120

= 0.8

 

Sorry if it's really badly explained (I tried ) Basically you should think of it as a tree diagram, but drawing a tree diagram would obviously take ages. I'm sure there are people here that could explain it much better than me.

[Ginger_Chris]

Simplest method:

 

p(picking at least one vowel) = 1 - p(not picking any vowels)

 

p(not picking any vowels) = 4/6 * 3/5 * 2/4 = 24/120 = 1/5 = 0.2

 

(This is found with a tree diagram, initially there are 4c's and 2 v's, so 4/6 chance of picking a c. Now a c has been removed there are 3 c's and 2 v's, a 3/5 chance of picking a second c. The chance of picking a final c is 2/4.) (c=consonant, v=vowel).

 

P(picking at least one vowel) = 1 - 0.2 = 0.8

 

Not much point worrying about combinations and permutations with this. Overcomplicating things a little, there are two groups, vowels and non-vowels, and the order you pick them makes no difference.

[Supergrunch]

I always find that probability confuses me, until someone like Chris comes out with a simplification that makes it obvious.

[The fish]

Each of the 6 cards has a different single letter on it. The letters are A B C D E and F. The cards are shuffled and then placed in a row.

 

(iii) The cards are now shuffled and placed face down. Three of the cards are selected at random. Find the Probablity that at least 1 of the cards selected is a vowel.

 

I'm a mechanics man myself (don't do stats anymore) but I'll give it a go:

I'll do it in reverse (ie finding the chance of not picking 1 vowel).

1st draw: 4/6

2nd draw: 3/5

3rd draw: 2/4

 

4/6 x 3/5 x 2/4= 24/120=1/5

 

Therefore, the chances of picking at least 1 vowel are 1-1/5=4/5=0.8

 

Ah, I see Chris and Zell got the same answer as me, I think we are, as a trio (especially Chris imo) fairly reliable...

[Supergrunch]

I dislike this sort of probability thing, and basic stats, but I find it can get interesting as it gets more advanced. Things like probability density functions are fun, and you can also do crazy things with moment generating functions.

[Chuck]

Does anyone work for AQA or OCR. I would like to buy some information from you

[Ginger_Chris]

Unfortunately not, I am applying to become a teacher (or at least do a PGCE) next year. So the more experience i get helping people the better (Physics rather than maths though :P).

 

Supergrunch; have you done anything on Probability Currents yet? I did them for Quantum mechanics a couple of years ago and still don't understand what they are or what use they have.

[DanielTimothy]

How would I factorise: x(squared sign) - 7x - 8, I don't get it, it doesn't have common factors! Ack!

[Supergrunch]

Supergrunch; have you done anything on Probability Currents yet? I did them for Quantum mechanics a couple of years ago and still don't understand what they are or what use they have.

Unfortunately not, I've never heard of them.

How would I factorise: x(squared sign) - 7x - 8, I don't get it, it doesn't have common factors! Ack!

Well, you need two numbers that make -8 when multipled together, and -7 when added together.

 

So, the pairs numbers that multiply to make -8 are: -8 & 1, 8 & -1, -4 & 2, 4 & -2.

 

Of these pairs, only -8 & 1 add together to make -7, so the factorised fraction is (x+1)(x-8).

 

This is pretty much the mental process I go through when doing these.

[Zell]

(x-8)(x+1)

 

I always factorise by trial and error in my head, but all you've got to think about is what two numbers add to make b and mutiply to make c (ax² + bx + c = 0). In this example the c value is negative, which means you're going to end up with one positive and one negative number.

 

EDIT: Beaten to it...

[MoogleViper]

² is alt+0178. Makes things easier to read than ^2.

[Zell]

You play Go Supergrunch, what rank are you? My friend is 12 kyu, although he's only been playing it for a year.

[DanielTimothy]

Thanks guys, I'm not dumb, just tierd.

[Supergrunch]

You play Go Supergrunch, what rank are you? My friend is 12 kyu, although he's only been playing it for a year.

12 kyu as well, after about 6 months.

[Atomic Boo]

Hello, I have some Geography homework that needs doing.

I have to write a couple of paragraphs about either the SF quake or the New Orleans hurricane. I have to choose the one which is a worse disaster and explain why the government's priority should be focused on that disaster.

 

Im stuck because im not sure which is worse. If someone could help to get me started please.

[DanielTimothy]

9. A shop buys a washing machine for £250 and sells it for £325. Work out the percentage profit.

You said 30 %

 

Its 33.33333333333etc% isn't it?

[Supergrunch]

9. A shop buys a washing machine for £250 and sells it for £325. Work out the percentage profit.

You said 30 %

 

Its 33.33333333333etc% isn't it?

Nope, it's exactly 30%:

 

325/250 = 1.3 so £325 is 130% of £250 and thus there is a 30% profit.

 

Done some proportion question so far so good bar this:

 

If y is inversely proportional to the square of x, write down an equation connecting x and y given that x = 2 when y = 3.5.

 

Could anyone walk me through it?

If y is proportional to x, this means y = kx. (where k is a constant)

 

If y is proportional to x², this means y = kx².

 

If y is inversely proportional to x², this means y = k/x²

 

Now we need to determine the value of k. We are given that x = 2 when y = 3.5, so:

 

3.5 = k/2²

 

k = 14

 

Therefore y = 14/x².

[Nucleus]

Rationalise the Surd:

 

2/(4+sqroot5)

 

Help plzzz.

[Ellmeister]

Rationalise the Surd:

 

2/(4+sqroot5)

 

Help plzzz.

 

Ok heres another go.

 

2/4+root5 multiply by the opposite (minus or positive sign) of the root.

 

So 2/4 + root 5 X 4- root5/4-root5 and I got 8-2root5/11.

 

Someone can come up with the correct answer and show me and nucleus how to do it

[Ginger_Chris]

Your Perfect right Elleister, You use the difference between two squares in reverse to eliminate the root at the bottom.

 

Using (X²-Y²)=(X+Y)(X-Y).

 

2 / (4+√(5));

multiply the top and bottom by the appropriate function;

=2*(4 - √(5)) / ((4+√(5))(4-√(5)))

multiply out the bottom using difference of two squares;

=(8-2√(5))/(4² - 4√(5) + 4√(5) - (√5)²);

=(8-2√5)/(16-5)

=(8-2√5)/(11)

It's all about remembering the difference of two squares, it also becomes useful for imaginary numbers (getting i's to the top) and simplifying nasty functions of cos, sin, cosh and sinh.