*made some important changes in 5-6 guesses*
Ok so for this module in my school, they employ this marking scheme for the MCQ exam called 'negative marking'. What this basically means is that for every correct answer we will get 1 mark, every wrong answer we will get -0.25 marks, and every blank we will not get any marks (or get 0 marks)
So comes the following question:
Would it better to leave any unsure questions blank, or simply guess all of them?
There should be a mathematical answer based on probability, so I shall set out to find this solution.
(all based on a 4-answer-choices MCQ)
The Basic Assumption
There is a basic assumption which we must make before we proceed, that is, there is a 1 in 4 chance of getting 1 mark, or 1/4 chance of getting 1 mark.
Some may be quick to point out that there are five options here, that is, 1 correct answer and 3 correct answers, AND the option of leaving it blank. Shouldn't it be 1/5?
The answer to that is simple, since leaving it blank is a definite 0 marks,(i.e. when you leave it blank, you KNOW for sure it is 0 marks, it is not a 1/5 chance that you will get 0 marks) it should be automatically excluded from the probabilities.
So with this basic assumption in mind, let's proceed.
Analysis
It is noteworthy that all the examples will just be weighing if it's better to guess all or to leave them all blank. They will not consider a 'mixture' of guessing and leaving blank, since that is a separate matter altogether.
So with the 1/4 assumption, it follows that
- for every 4 guesses, you will get 1 correct.
Since the 4 guesses are for 4 random questions, this has to be correct; it is mathematically sound.
Let's start with a simple example, there are only 4 unsure questions and hence only 4 guesses you make in the paper.
4 guesses - 1 correct, 3 wrong
-> +(1x1) -(3x0.25) = +0.25
Thus, more beneficial to guess all.
How about 5 guesses? This would be slightly more complicated, since 1/4 of 5 is 1.25, and rounding up or down would result in an inaccurate answer.
To get a round number, we take a group of 4 people with 5 guesses each. Thus 'getting 0.25 correct' means out of a group of 4 people, 1/4 of them will get it right (means they have TWO correct) while the other 3/4 of them will get only one right.
[Read the explanation in these square brackets if you don't get why it's 3/4 will only get 1 right.
Let's simplify matters to just 4 people having 1 guess each. If they each have a 0.25 chance of getting it right, it means 1 out of 4 will get it right.
So why that 1/4 group in the example above gets TWO correct is because their odds state they will get the 1st '1' correct, just that the 2nd '0.25' is up for probability]
Thus for 5 guesses, there's a 1/4 chance we will get 2 correct (better to just guess all)
and there's a 3/4 chance we will only get 1 correct (better to just leave all blank, as 1 correct in 5 means +1 -1.25 = -0.25)
Therefore, for 5 guesses, there is a higher probability that you will get a negative mark than a positive mark for guessing.
HOWEVER. What you should do here is to leave 1 of them blank (to guarantee 0 marks, no negative), and guess the other 4 (which will be the same case as 4 guesses, which is beneficial as shown earlier.)
6 guesses will follow the same logic, leave 2 blank, and guess 4.
7 guesses onwards it is more beneficial to go for the +0.75 (you have a higher probability anyway) than to settle for the +0.25 of 4 guesses, 3 blank. Thus:
7 guesses (instead of 7 blanks) will result in a higher chance of getting +0.75 than the negative case (work it out yourself), same for 8 and 9 guesses.
10 guesses is another 50/50 chance as in the 6 guesses case, but this time it's either a positive or neutral (0 net marks) result, so it's better to take your chance and guess them all too.
And by further deduction you can see that subsequent greater number of guesses will always result in a higher probability of getting a positive mark. Thus for 7 guesses and above, it is more beneficial to guess all than to leave all blank.
Now let's take a step back and examine the last 3 numbers which we did not look at - 1, 2 and 3 guesses.
1 guess
You have a 1/4 chance of getting 1 mark, and a 3/4 chance of losing 0.25 marks. It's a no-brainer, better to just leave it blank and guarantee no negation since the negative result has a higher probability.
2 guesses
We have to look at this in the case of multiple participants again, since 0.25 x 2 = 0.5
So out of 2 participants, it follows that either one will get it correct. It's another 50/50 case.
50% -> You get 1 mark
50% -> You lose 0.25 marks
This is the only ambiguous case, where the advantage of securing '0 points' by not guessing at all is not clear.
3 guesses
0.25 x 3 = 0.75
Which follows that there is a higher probability that you will be in the group that gets 1 /3 correct (3/4 chance to be exact) which is a +1 - 0.5 = +0.5 benefit, hence it is better to guess all for 3 guesses.
Summary
If you have 1 unsure question, it is more beneficial (or mathematically sound) to leave it blank.
If you have 3,4 unsure, guess them all.
If you have 5 or 6 unsure, leave blank 1 or 2 respectively, and guess the remaining 4.
If you have 7 or more unsure questions, it is more beneficial (or mathematically sound) to guess them all.
If you have 2 unsure.. flip a coin to decide whether you should guess or not, as there is no clear mathematical advantage on either side.
P.S.
Weiqin did a binomial calculation that more or less supports my noob calculations
http://i136.photobucket.com/albums/q166/atqhteo/31082010336.jpg
http://i136.photobucket.com/albums/q166/atqhteo/31082010337.jpg
ENJOY :D
Monday 30 August 2010
Friday 27 August 2010
(not) my psych mid term paper
Describe three views on neural correlates of human intelligence. Which according to your view is the most plausible?
They are namely the side view, the top view, and the cross-sectional view. If we look at it from the side view, 'neural correlates of human intelligence' looks like this
[]
And clearly this isn't a very good view, so we will put this on hold for the time being.
A second view is the top view, more popular than the side view because 'top' has fewer letters than 'side'. Also, 'top' is also a synonym for 'best', thus it lends credibility to its claim to be the best view. Just for illustration's sake, this is what the top view looks like
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
assuming very skinny letters of course.
And last but definitely not the least, which is what i believe is the best view of them all, is the cross-sectional view.
Now why do we think this is the best view (or rather why I think, and will hence try to make you think so because that's the point of writing such a paper. If I'm just trying to make myself think then I wouldn't be writing a paper, I will be talking to myself, which is what I'm doing in these parenthesis. Now isn't that an interesting word, 'parenthesis'. Doesn't really make any sense how it was formed. Like was it the thesis of some parent? anyway, i better get back to the topic at hand before you get bored)
As i was saying before i was so rudely distracted by my own mind, the cross-sectional view is the best one of them all. Not only does it have the most cool sounding name , it has the word 'cross' in it. Cross of course refers to the christianity, which of course means it is a very holy word.
But of course with a proper dictionary we all know it means (dictionary.com, 2010)
Thus if you see a Boeing 707 flying and it cuts a kite into half, at right angles of course, that is a cross section.
So you may ask, what exactly does it look like? of course it looks like this
[ ]
As we can see, this is clearly the best view of them all, although it looks slightly similar to the side view. This is because this has more space in between them, and we all know that space is the most important thing in the world today due to overcrowding.
In conclusion, I think it is essential we do not just take one view in isolation as that is never good. It is always best to take many views and unite them and get them to sing a song of unity to prove it and look at it on a whole, not as a half.
Thus concludes my brilliant term paper which you will give me full marks for because you are utterly blown away by my spectacular intelligence.
Neural correlates on human intelligence refers to how our neural co-relates to human intelligence. A simple comparison can be made on the number of letters. Since neural has 6 letters and human intelligence has 20 (i can't really count very well that's why i'm doing psych), we can see no real relationship. Also, a human isn't really intelligent if not he wouldn't have to write this paper because he would know everything.
They are namely the side view, the top view, and the cross-sectional view. If we look at it from the side view, 'neural correlates of human intelligence' looks like this
[]
And clearly this isn't a very good view, so we will put this on hold for the time being.
A second view is the top view, more popular than the side view because 'top' has fewer letters than 'side'. Also, 'top' is also a synonym for 'best', thus it lends credibility to its claim to be the best view. Just for illustration's sake, this is what the top view looks like
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
assuming very skinny letters of course.
And last but definitely not the least, which is what i believe is the best view of them all, is the cross-sectional view.
Now why do we think this is the best view (or rather why I think, and will hence try to make you think so because that's the point of writing such a paper. If I'm just trying to make myself think then I wouldn't be writing a paper, I will be talking to myself, which is what I'm doing in these parenthesis. Now isn't that an interesting word, 'parenthesis'. Doesn't really make any sense how it was formed. Like was it the thesis of some parent? anyway, i better get back to the topic at hand before you get bored)
As i was saying before i was so rudely distracted by my own mind, the cross-sectional view is the best one of them all. Not only does it have the most cool sounding name , it has the word 'cross' in it. Cross of course refers to the christianity, which of course means it is a very holy word.
But of course with a proper dictionary we all know it means (dictionary.com, 2010)
"a section made by a plane cutting anything transversely, esp. at right angles to the longest axis."
Thus if you see a Boeing 707 flying and it cuts a kite into half, at right angles of course, that is a cross section.
So you may ask, what exactly does it look like? of course it looks like this
[ ]
As we can see, this is clearly the best view of them all, although it looks slightly similar to the side view. This is because this has more space in between them, and we all know that space is the most important thing in the world today due to overcrowding.
In conclusion, I think it is essential we do not just take one view in isolation as that is never good. It is always best to take many views and unite them and get them to sing a song of unity to prove it and look at it on a whole, not as a half.
Thus concludes my brilliant term paper which you will give me full marks for because you are utterly blown away by my spectacular intelligence.
Sunday 22 August 2010
let's all waste time with haiti
So, after reading about Singapore's bravado in the YOG soccer quarterfinals, demolishing Montogeremy(howtospell) 3-0, and how we have some influential playmaker who connects very well with the striker because they have been playing since young, obviously I did get a little hyped about the whole soccer thing.
So at 8.40PM i plonked in front of my TV and supported the bunch of young boys kicking the ball; OUR bunch of young boys kicking the ball around, expecting to see some wizardry.
The first half was quite entertaining, with some BRILLIANT chances for Singapore.. who promptly missed about 3 OPEN goals. Yes, wide open goal but the receiving player could not head the ball down properly. Maybe it was too high.. maybe he is not used to headers.. maybe because he's only 14? -shrugs.
Whatever the case, I, as the couch soccer critic, is always correct right?
Anyway, in the last 5 minutes of the half, 2 dumb things occured.
Dumb Thing Number 1) For no real reason, after a slight collision in midair between the Singapore goalie and a Haitian striker, the goalie appears riled and steps up into the face of the Haitian to challenge him.
Could have easily been a yellow card for the goalie, but the referee just gives him a warning. Furthermore the goalie's face super cockyarrogant type, so makes him look more dumb and annoying.
Dumb Thing Number 2) After a Singapore substitution, a Haitian player turns past a Singaporean defender and fires a weak shot towards the goalie. Instead of catching it comfortably, he chooses to deflect the ball, even though it was flying straight at him. The ball flew into the oncoming path of a Haitian striker who wasted no time to drill the ball into the goal with his head.
Haiti 1, Singapore 0
Ok so that wasn't what made me make this blog post. It was the second half.
Before we go to that, here is what I believe the Haitian coach told his players in the dressing room during half time:
"Ok guys, good job grabbing that fluke goal despite Singapore dominating most of the first half. Now we have to do what we do best, WASTE TIME. I want every single one of you to waste as much time as possible. Fall to the ground and stay down longer, fake every possible injury as you can from head to toe, be creative!
I want all of you to clock at least 60 seconds each lying on the ground! And you better not let me see any of you run for a throwin/goalkick that is ours. Take your time!
And goalie, if you can do 10 stepovers on the ball before getting carded, I'll treat you to lunch tomorrow!"
So with that motivational speech, the Haitian players went out and DID JUST THAT.
To say the second half was painful to watch is an understatement. It was probably the most frustrating 40 minutes (YOG is only 40 mins a side) of soccer I've watched?
The Haitians were doing everything in the book to waste every second of time possible. Their players started rolling around on the floor after any slight challenge, grabbing random parts of their body and asking for a stretcher... DAMN ANNOYING. Like seriously if i was the paramedics carrying the stretcher i'll just 'oops' -drops player-
they kept this up for the whole entire 40 minutes. I was surprised the referee waited about 20+ minutes before starting to take out the yellow cards.
And the Haitian goalie.. oh wow. It started off with some casual strolling to retrieve a ball for a goalkick. Then on another possession he added a stepover when he was retrieving the ball for a goalkick. Then the last straw was on one occasion when he just casually strolled to get the ball, then on the way back he did multiple stepovers and casually pulled the ball around.
LIKE SERIOUSLY??!?
For that last instance the referee wasted no time running over to show him a yellow card - AND HE SARCASTICALLY APPLAUDED THE REFEREE - wtf??? isn't this an automatic second yellow card and a red? I know in NBA players will get a technical (or a 2nd one) if they applaud in mockery like that.
SRSLY. just book the whole damn haitian team so they will all be ineligible for the finals match and Singapore will go and take their place.
Super ridiculous man. Twitter is ablaze with hateful mean comments towards the Haitians and some are really quite bad.(as you can guess, many are related to the earthquake of course) I am tempted to throw in a couple of my own but.. I shall maintain my niceness. rawr.
K i better get to sleep, 10 hour day tomorrow. nite.
So at 8.40PM i plonked in front of my TV and supported the bunch of young boys kicking the ball; OUR bunch of young boys kicking the ball around, expecting to see some wizardry.
The first half was quite entertaining, with some BRILLIANT chances for Singapore.. who promptly missed about 3 OPEN goals. Yes, wide open goal but the receiving player could not head the ball down properly. Maybe it was too high.. maybe he is not used to headers.. maybe because he's only 14? -shrugs.
Whatever the case, I, as the couch soccer critic, is always correct right?
Anyway, in the last 5 minutes of the half, 2 dumb things occured.
Dumb Thing Number 1) For no real reason, after a slight collision in midair between the Singapore goalie and a Haitian striker, the goalie appears riled and steps up into the face of the Haitian to challenge him.
Could have easily been a yellow card for the goalie, but the referee just gives him a warning. Furthermore the goalie's face super cockyarrogant type, so makes him look more dumb and annoying.
Dumb Thing Number 2) After a Singapore substitution, a Haitian player turns past a Singaporean defender and fires a weak shot towards the goalie. Instead of catching it comfortably, he chooses to deflect the ball, even though it was flying straight at him. The ball flew into the oncoming path of a Haitian striker who wasted no time to drill the ball into the goal with his head.
Haiti 1, Singapore 0
Ok so that wasn't what made me make this blog post. It was the second half.
Before we go to that, here is what I believe the Haitian coach told his players in the dressing room during half time:
"Ok guys, good job grabbing that fluke goal despite Singapore dominating most of the first half. Now we have to do what we do best, WASTE TIME. I want every single one of you to waste as much time as possible. Fall to the ground and stay down longer, fake every possible injury as you can from head to toe, be creative!
I want all of you to clock at least 60 seconds each lying on the ground! And you better not let me see any of you run for a throwin/goalkick that is ours. Take your time!
And goalie, if you can do 10 stepovers on the ball before getting carded, I'll treat you to lunch tomorrow!"
So with that motivational speech, the Haitian players went out and DID JUST THAT.
To say the second half was painful to watch is an understatement. It was probably the most frustrating 40 minutes (YOG is only 40 mins a side) of soccer I've watched?
The Haitians were doing everything in the book to waste every second of time possible. Their players started rolling around on the floor after any slight challenge, grabbing random parts of their body and asking for a stretcher... DAMN ANNOYING. Like seriously if i was the paramedics carrying the stretcher i'll just 'oops' -drops player-
they kept this up for the whole entire 40 minutes. I was surprised the referee waited about 20+ minutes before starting to take out the yellow cards.
And the Haitian goalie.. oh wow. It started off with some casual strolling to retrieve a ball for a goalkick. Then on another possession he added a stepover when he was retrieving the ball for a goalkick. Then the last straw was on one occasion when he just casually strolled to get the ball, then on the way back he did multiple stepovers and casually pulled the ball around.
LIKE SERIOUSLY??!?
For that last instance the referee wasted no time running over to show him a yellow card - AND HE SARCASTICALLY APPLAUDED THE REFEREE - wtf??? isn't this an automatic second yellow card and a red? I know in NBA players will get a technical (or a 2nd one) if they applaud in mockery like that.
SRSLY. just book the whole damn haitian team so they will all be ineligible for the finals match and Singapore will go and take their place.
Super ridiculous man. Twitter is ablaze with hateful mean comments towards the Haitians and some are really quite bad.(as you can guess, many are related to the earthquake of course) I am tempted to throw in a couple of my own but.. I shall maintain my niceness. rawr.
K i better get to sleep, 10 hour day tomorrow. nite.
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