Great Western Coffee Shop

ok, there is a quiz every sunday at our local... at the end there is something called the ''lucky three'' basically out of the 40 questions 3 are picked and they say right or wrong... simple huh? well the argument arised what is the chance in winning the lucky three (excluding the fact that if it is a draw it rolls over)

WHAT!

I'm a mathmeticia but I dont get the parameters!

3 Q's are picked so there is a 3/40 chance of being picked

Is there any rule about what is right or wrong?

i think this is where the argument arrised! all the teams playing have a chance in the lucky 3 at the end... three random questions are picked (in the hat there are 80 pieces of paper for example question 1 correct and question 1 wrong and so on) what is the chance of matching correct or incorrect on the 3 questions

my friend thinks it is 1/8 (which would be correct if there were only 3 questions) but does the fact that the 3 questions are picked out of 40 change these odds?

i myself think that the chance is 1/240

Still not quite sure what you mean?

What is actually drawn out of the hat a question or an answer or question and answer?

What do you have to guess?

Also:

Are there an equal number of right and wrong pieces of paper? If not you would need to know the ratio and have to calculate the odds accordingly.

Are the questions returned to the hat after each pick,  each team or do they stay out.

If they are returned after each pick you are always selecting out of 80.

If they are returned after each team you are selcting out of 80, 79, 78.

If they are kept out it would depend on what order the teams draw the questions as you would be drawing from a dimissing pool.

As far as I can see your friend is right if there are 80 bits of paper with an equal number of right and wrong and the paper is returned after each pick. Because you have a 0.5 chance of being right on the first, 0.5 chance on the second and 0.5 on third.

Thus 0.5* 0.5*0.5 = 0.125

It's a varient on the coin tossing, but confused by the pair of socks from a drawer. For coin tossing each throw is always 50:50 no matter how many heads you've thrown before. Drawing a matching  pair of socks from a drawer with an equal number of blue and black is 3 if you don't mind  whether it's blue or black, in this case however you do mind what the answer is, so it starts at 50:50 but depending on whether the paper is replaced or not gets more complicated with subsequent picks.   

Now if the paper isn't replaced then it's still 0.5 for first go but 39/79 for second go if you are guessing your 2nd answer to be the same as the first actual or 40/79 if you are guessing the opposite to first actual answer. For the third it could be 38/78 if first two actual answers are the same as your third guess but  39/78, if the first two actual answers are different.

So still hovering around an eighth.

It gets more complicated for later teams if the paper is removed at each go. If you've guessed more of the opposite answers to those drawn so far then your odds are better  than an eigth because there are more of your answers left in the hat. Conversley if your guesses match those drawn so far there are less bits of paper with your answers in hat so the odds lengthen.

Perhaps Mookiemoo can pick holes in my logic.

Relex109, I'm haveing trouble working out the parameters too ... and I've done a bit of maths and stats in my time.   Googling for "Lucky Three" didn't help ... gave me so 3 minutes films and the "Lucky Three DimSum Bar" in Fall Church, Washington DC ... which at least gets me back on track via the Orange line of the Washington Metro.   I'm a long way from "The West" ... but am I the only one who's got off at Rosslyn just to ride up and down the longest escalators that I know of anywhere!

If it's a question of guessing which question is pulled and in the right order, the answer is 1/40 x 1/40 x 1/40 if all three questions have to be guessed before the first draw is made, or 1/40 x 1/39 x 1/38 if the team makes a guess, a question is drawn, guesses, etc

If it's simply whether the team got three questions questions chosen at random from those asked during the quiz right or wrong, then there is easy statistical answer as it depends on the skill of each of the teams in answering the questions (i.e. the average score for the teams will be a factor) ...

Or mine!

at the end of the quiz three numbers relating to the quiz questions are pulled out of the hat within the hat each question has 2 pieces of paper one for correct and one for incorrect... but the same number cant be selected twice so if say for example 1 is pulled out twice first time correct and second time incorrect then the second 1 is discarded and another number drawn

i know that if there were only 3 questions then the chance would be 1/8 as there are 8 combinations across the 3 questions

yyy
nnn
yny
nyn
yyn
nny
nyy
ynn

but is the fact that there are 40 original questions out of which the 3 are selected irelevent as my friend belives

i really have a headache over this  :D

...sorry Grahame, but last October I stayed in Rosslyn for a week and rode the escalator ever day to get into Washington DC... so you're now not the only one.. :) ;)

I think all of you need to get out more!  :o ::) ;D

If I could understand the question I might!

give up!  :'(

Relax - WHAT exactly happens

Are there questions in the bag or answeres?  Are there two bags - one with Q's and one with answers - because one post you made implied the Q's and answers were in ther same bag!

For things like this I am like a dog with a bone

OK, o I've been trying to ignore this one, but I did Maths as a degree, so now I need to know too..

We need to know more specifics... please?  well I do anyway to understand it..  :)

ok the lucky three is done after the quiz there are 40 questions in the quiz now say you answer question 4 correct question 2 wrong and question 40 wrong, if the quiz master pulled out 4 correct 2 wrong and 40 wrong you would win but if for example they pulled out 40 correct you would lose

Right - so there are 40 questions in the quiz then at the end there is a random draw and it has to match the answer you give for that Q!


I PAss

I'm not a statitistian (sp?)

Because I do not know what you answered in the quiz

Pass - I suspect about the same chances of he national lottery

well bear in mind that once the quiz is over and the lucky three starts there are only 2 answers for each question correct or incorrect

I think I get what relex109 is saying about the lucky three so here goes.

Assumming you are reasonably good at quizes then you will have more questions right than wrong so drawing  "Question  N wrong" is more likely to eliminate you as opposed to drawing "Question N right". So do the odds will vary in proportion the number of questions you have right out of 40?

If you got all 40 original questions right then it's as relex 109 says:


The same odds would apply if you got all 40 original answers wrong.

But how you work out the odds for any other combination of right and wrong quiz answers? There are now 6 out of the 8 possible selections which afffect the odds. If you have more right than wrong in your original answers then the 3 selections with 2 rights should increase your chance of winning, but the 3 selections with 2 wrongs are more likely to cause you to lose.

So do they even out?

Are we back to simple penny tossing?

Selection 1 Question X  win or lose i.e. 50:50 (if you lose on this round then you are out and further selections are irrelevant)
Selection 2 Question Y  win or lose i.e. 50:50 (out if you lose)
Selection 2 Question Z  win or lose i.e. 50:50 (out if you lose)

So is it back to 0.5*0.5*0.5= 0125 or 1/8?

Where it all started.

My brain hurts?


















 

i really cant take my mind off this, who would have thought i would get so obsessed about mathmatics

I'm going to refer this to a maths and computing forum I frequent for their learned opinon!

Will post results

Thanks Mookiemoo It's got me beat will look forward to the results.

Did we ever solve this...?! :o ::)

the more i think about it, the more i belive it is actually 1/8 so you have a 12.5% chance of winning it...

im pretty sure now that the fact that the 3 questions picked out of the 40 original doesnt matter so you are just left with a 50/50 chance on each of the 3 questions as you have to get all three matched it means 0.5x0.5x0.5=0.125----- 12.5% or 1 in 8

my head still hurts tho

Having tried several ways through the problem, see previous posts, I agree with relex109 that 1/8 seems to be the answer.

However, if someone could supply a definative answer it might stop my head hurting.