Basic Math a Little Beyond the Comprehension of Most British MPs

Ok everyone, time for a quick math quiz. 

If a coin is flipped twice, what is the probability that it will come up heads both times? I understand that afternoons can be draining, so please feel free to say you don't know. 

The answer is of course 1/4, or 25 percent. One might hope that this basic grade school level arithmetic might not be beyond the abilities of politicians who manage national budgets, wage war, and run prisons, schools, and hospitals. 

Alas, this is not the case.

Ninety-Seven of the House of Commons' 650 Members of Parliament were asked the question above by Ipso Mori. Only 23 percent of Labour MPs and 53 percent of Conservative MPs answered correctly. Amazingly, 45 percent of polled MPs claimed that the answer was 50 percent. Perhaps most depressingly is how confident MPs said they were in their numerical skills, with 76 percent of Tories and 72 percent of Labour MPs saying that they were confident when dealing with numbers. It is of some reassurance that seven percent of MPs were ok saying that they did not know the answer.

These figures really shouldn't surprise us, especially when one considers how good British politicians are at screwing up the economy. 

Indeed, the exact size of the UK's debt (and indeed the difference between the debt and the deficit) baffles a frightening number of MPs. A particularly scary part of Britain's Trillion Pound Horror Story illustrates this point from 07:20:

Of course, it's not just the politicians who are misinformed or arithmetically challenged, the great public here and in the UK leave a lot to be desired. As Bryan Caplan has pointed out, even those of us who think we are rational when it comes to voting and the economy are far from impressive. 

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  • Tulpa Doom||

    If a coin is flipped twice, what is the probability that it will come up heads both times?

    Depends on the weight distribution of the coin and whether both sides are heads or both sides are tails, etc. Most coins are not fair coins (ie, equal prob of heads or tails) due to imperfections in manufacture.

  • ||

    If Tulpa responds to a question in a retarded manner, what is the probability that that response will be super retarded each time?

  • Tulpa Doom||

    Clear thinking is for statists, or something. You keep fighting the man with your imprecise statements, Epi!

  • ||

    ONE HUNDRED PERCENT

  • ||

    P(Tulpa is a dipshit) = 1.5

  • tarran||

    No Epi!

    He's technically correct! Which, as everyone knows, is the best kind of correct!

  • ||

    Warty! Bring me the forms I need to fill out to have tarran taken away!

  • tarran||

    Episiarch,

    You completed your reply one minute early. I am demoting you!

  • ||

    Demote NutraSweet, he was the one who got beaten like a rented mule.

  • SugarFree||

    "Guards! Bring me the forms I need to fill out to have her taken away!"

  • SugarFree||

    I see I can't out-glib him in dated Futurama references.

  • Scruffy Nerfherder||

    Technically correct gets all the ladies, 60% of the time, all the time.

  • Aresen||

    Depends on the weight distribution of the coin and whether both sides are heads or both sides are tails, etc. Most coins are not fair coins (ie, equal prob of heads or tails) due to imperfections in manufacture.

    While this is perfectly correct, it misses the fact that the question says 'a coin' and does not describe what, if any, imperfections or unequal weight distributions may exist.

    Since the 'bias' of the coin is unknown, it must be ignored for the purposes of the question and the 1 in 4 probability is therefore correct based on the information available.

  • Tulpa Doom||

    Since the 'bias' of the coin is unknown, it must be ignored for the purposes of the question

    I disagree. You can't assume the coin is fair just because you're not told whether it is.

  • Tulpa Doom||

    Arithmetic is what most people think of when talking about "dealing with numbers". Probability theory is an application of math, not math itself.

  • kinnath||

    This is trolling, right?

  • Killazontherun||

    Of course it is, he is a Jesuit, right? That's what they do, history's biggest trolls.

  • Trespassers W||

    +0.5

  • Trespassers W||

    The only alternative is that Tulpa isn't as smart as he thinks he is, and I, for one, don't want to live in such a world.

  • Tulpa Doom||

    Word definitions matter. If they don't want to be corrected, maybe they shouldn't put "basic math" in their headlines and ask questions about "dealing with numbers" when the thing they're analyzing is not really in either category.

  • Fluffy||

    Thank you for explaining to me that probability theory is not part of math.

    Also not part of math? Geometry.

  • Trespassers W||

    Also group theory, which, by the way, is just a theory.

  • Stormy Dragon||

    You know who else had theories about groups...

  • Ted S.||

  • Fluffy||

    The only way I can understand this is if somehow respondents thought they were being asked what the odds were that you'd get the same result twice in a row.

  • Tulpa Doom||

    Or if they weren't listening carefully to the question. That would explain some of the 1/2 answers, methinks.

    What they should have done would be to ask both the probability of one head in one flip, and the probability of two heads in two flips.

  • Rights-Minimalist Autocrat||

    You are being far too generous.

  • SugarFree||

    Idiocy is also an explanation.

  • ||

    I dunno, dude. An inability to parse the question is even more embarrassing than an inability to calculate .5^2.

  • ||

    Yes, but if a tree falls in the forest and no one is there to hear it, is Tulpa retarded?

  • SugarFree||

    Does the tree have imperfections that would cause it to fall silently?

  • Fluffy||

    What's the weather like that day?

  • ||

    It depends on if Tulpa is retarded, so...yes?

  • SugarFree||

    The whole tree thing never made any sense to me. Sound is not an observer-mediated event. Trillions of sounds are made every day that no human is hearing. Solipsistic trash.

  • Fluffy||

    The question revolves around whether the definition of sound is "vibrations in the air or another medium" or "vibrations in the air or another medium that hit an eardrum in a living creature".

  • nicole||

    Fluffy is right, but did anyone anywhere ever think "sound" did mean "vibrations in the air or another medium that hit an eardrum in a living creature"?

  • Fluffy||

    Fluffy is right, but did anyone anywhere ever think "sound" did mean "vibrations in the air or another medium that hit an eardrum in a living creature"?

    Philosophers did.

    It's like asking if all life everywhere disappeared, would Mars still be red?

    "Red" is "light of a certain wavelength hitting an eye." It's a visual phenomenon, so if all eyes vanish, it can be said to no longer exist. The universe would be blind, so nothing would be red any more.

  • Heroic Mulatto||

    "Red" is "light of a certain wavelength hitting an eye." It's a visual phenomenon, so if all eyes vanish, it can be said to no longer exist. The universe would be blind, so nothing would be red any more.

    You disgusting Qualiaphile!

  • Killazontherun||

    "Red" is "light of a certain wavelength hitting an eye." It's a visual phenomenon, so if all eyes vanish, it can be said to no longer exist. The universe would be blind, so nothing would be red any more.

    In a biology class in college I purposely gave Augustine's explanation of how light is processed in the eye just to let the professor know he wasn't the boss of me.

  • Tulpa Doom||

    "Red" is "light of a certain wavelength hitting an eye."

    A common problem in robotics is to have the robot open up a box of balls and pick out the red ones. Easy as pie for humans to do, because our brains automatically take into account changes in lighting when determining color. Not so easy for computer vision.

    A good question would be whether a red ball is still red when it's in a completely dark room. Depends on the definition; I would say that color is best defined as the wavelength of light (or combination thereof) that the surface most easily reflects when bombarded with all wavelengths of light (ie continuous spectrum of white light). In which case, the color would not change when the light was turned off or if the quality of the light changes.

  • ||

    Tulpa may be solipsistic but even I wouldn't go so far as to call him trash, NutraSweet. That's pretty harsh.

  • Pro Libertate||

    That would impress me if you weren't just a construct in my mind.

  • Tulpa Doom||

    What's especially funny about this attempt to be a jerkface on you guys' part is that it's the imprecise words that make that a supposedly unanswerable question. Thanks for making my point about the importance of precision in language.

  • Ayn Random Variation||

    Probability that an American citizen gets this question right?

    10%?

  • Tonio||

    Probabilities are generally expressed as decimals, ie 0.10, instead of as percentages.

  • ||

    That's Mary playing nice, dude. Just ignore her.

  • Tulpa Doom||

    Huh? They're commonly written as fractions and odds as well as percentages. When you're doing computations they're almost always converted to a real in [0,1] but expressing them in other forms makes sense depending on the context.

  • purple_persuader||

    There are only three scenarios possible, so how is it 25%? It's either heads/heads, tails/tails or heads/tails(order may vary).

  • Almanian's Evil Twin||

    Order matters

  • Tulpa Doom||

    Actually the way the question is framed, order doesn't matter (they're only asking about how many heads there were). Our usual method of analysis is to convert it to an equivalent problem where order does matter (ie, what is the probability that coin 1 comes up heads AND coin 2 comes up heads). This is sensible because there's only one outcome in that problem that corresponds to 2 heads.

    The gremlin here is that in the original question, the three possible "head counts" don't have equal probability.

    If the question were, if you flip 8 fair coins what is the probability that 4 come up heads, then it would be more difficult to approach it by looking at every outcome in the "order matters" problem that results in 4 heads. You'd have to look at it as an "order doesn't matter" binomial distribution problem to get 8!/(4! 4! 2^8) = 35/128.

  • db||

    0.5 *0.5 = 0.25

  • db||

    The overall probability is equivalent to the product of the probabilities of independent trials.

  • Spoonman.||

    Please tell me you're joking.

  • ||

    GET THIS MAN A SEAT IN PARLIAMENT

  • kinnath||

    heads/heads; heads/tails; tails/heads; tails; tails.

    FOUR possible outcomes.

  • Tonio||

    Purple is describing combinations (order doesn't matter) and Kinnath is describing permutations (order matters). But you're both too deep in the weeds here.

    FTFA: A total of 97 MPs were asked this probability problem: if you spin a coin twice, what is the probability of getting two heads?

    The point is the innumeracy of british politicians.

  • Trespassers W||

    You wanna bet?

  • Rasilio||

    There are 4 possible outcomes.

    Flip 1 = A
    Flip 2 = B

    Heads = H
    Tails = T

    The possible options are
    AHBH
    ATBT
    AHBT
    ATBH

    2 of them happen to result in Heads/Tails combo but that extra result cannot be ignored and only 1 of the 4 possibilities results in Consecutive heads options.

  • BoscoH||

    Conclusion:

    Retarded Conservatives Liberals.

  • BoscoH||

    Let's try this again:

    Conclusion:

    Retarded Conservatives Liberals.

  • BoscoH||

    And again:

    Retarded is-greater-than Conservatives is-double-greater-than Liberals.

    Hit and Run Comments is-tripple-greater-than BoscoH.

  • Tonio||

    Newspeak superlatives (ascending order):
    Good
    Plus Good
    Double Good
    Double Plus Good

    Going back to my clove-flavoured gin, now.

  • ||

    Clove-flavored? Weird. Got a link? I'm almost through my current bottle of Crater Lake.

  • Tonio||

    Epi, AFAIK, there is no actual clove-flavored gin. This was a reference to 1984 where clove-flavored gin is the house special at the Chestnut Tree Cafe where Winston hangs out after he's been tortured.

  • ||

    Well now you've gone and made me look the fool, Tonio!

    I guess I'll just get more Crater Lake.

  • ||

    I'd be wary of drinking anything from Crater Lake given what's been pooping in there.

  • Rights-Minimalist Autocrat||

    You can't triple stamp a double stamp!

  • DRM||

    So . . .

    Retarded › Conservatives » Liberals

  • Tim||

    100% If you are Bill Clinton, you will always get head.

  • NoVAHockey||

    and tail

  • Pro Libertate||

    And he's a Rhodes Scholar, which means that he uses British math.

  • db||

    FOR BRITISH EYES ONLY!

  • BakedPenguin||

    Mr F.?

  • nicole||

    Mr MP, in this case.

  • Fluffy||

    Sometimes the inability to do math can HELP you, though.

    For example, the British ruled India for a very long time because they were unable to understand that a few hundred thousand Brits just simply could not rule over hundreds of millions of Indians.

    "Oy, guv'nor! Dey've oinly gots us two or three to one!"

  • Fluffy||

    They were no doubt aided in this productive ignorance by the presence of large numbers of Scots in their ranks. Scots notoriously can't even count to five.

  • Pro Libertate||

    Scots like. . .Adam Smith?

  • Fluffy||

    His father was cuckolded by a Norwegian.

  • SugarFree||

    [gasp] That means he's basically a Laplander!

  • Pro Libertate||

    Same thing. Scots are mostly half-Dane by right of rape, anyway.

  • ||

  • tarran||

    Scots notoriously can't even count to five.

    They don't need to.

    One day a Brit Gen'ral is marchin' along wit' his regiment. After a bit they come across a hilloc and atop it is this braw scottish warrior holdin' a huge claymore above 'is 'ead. And 'e yells down at them "Ahm Red Rory o' the Glen! Send up your best man!"



    An' Gen'ral purples a wee bit, an' he turns to his Adjant an' says, "Adjunt! Send up you're best man! I wan' that man head!" And up goes the best man and then theres bangin' and bashin' and sqwackit and screamin' and then cloppity cloppity clop comes down the 'ead of the best man.

    An' Red Rory stands on top o 'the hilloc and shouts. "Ahm Red Rory o' the Glen! Send up your best squad!"

    An' the Gen'ral purples a bit more, an' he turns to his Adjunt an' says, "Adjunt! Send up your best squad! I wan' that mans Head!" And up goes the best squad an' then theres bangin' an' bashin' an' sqwakit an' screamin' an' then cloppity cloppity clop comes down the 'eads of the best squad.
  • tarran||

    An' Red Rory stands on top o' the hilloc and shouts. "Ahm Red Rory o' the Glen! Send up your best comp'ny!"

    An' the Gen'ral purples a lot more, an' he turns to his Adjunt an' says, "Adjunt! Send up your best comp'ny! I Wan' that mans HEAD!" And up goes the best comp'ny an' then theres bangin an' bashin' ab' sqwakit an' screamin' an' then cloppity cloppity clop comes down the 'eads of the best comp'ny.

    An' Red Rory stands on top o' the hilloc and shouts. "Ahm Red Rory o' the Glen. Send up the whole regiment!"

    And Gen'ral turns completely purple, an' he turns to his Adjunt an' says, "Adjunt! Send up the Whole Blawdy Regiment! I WAN' THAT MANS HEAD!" And up goes the whole regiment and there's bangin' an' bashin' an' sqwakit an' screamin' goin' on for the better part o' an hour or so, an' suddenly the Adjunt comes runnin' down the hill yellin'

    "Run sir, run! It's ae ambush! There's two ae them!"
  • Mickey Rat||

    Mr. Scott would like to have a word with you:

    "You mind your place, mister, or you'll be wearing concrete galoshes."

  • ||

    On the Day of Judgment, I will rejoice when God condemns the jackass who invented the phrase "Please do the needful." Also, it's "chree", not "three".

  • Ken Shultz||

    I suspect they were confused by the old example about how the odds of heads on the second toss are the same as the first.

    Maybe it means that Labor is more ideological than the Tories. Labor MPs, anyway, appear to be more likely to remember an adage and advance it as fact. Tories are more apt, apparently, to work out the answer for themselves.

    Incidentally, I think Tories tend to think people should be responsible for solving their own problems, too. I don't know whether this is emblematic of anything, but if if confirms my preconceptions, then it must be true!

  • Scruffy Nerfherder||

    I suspect they were confused

    You could have stopped right there.

  • Hyperion||

    The limeys are just hopeless. It is just better for them if too many folks get on one side of the island and it tips over and drowns them all, putting them out of their misery. They still need a queen for christs sake, fucking middle ages luddites.

    Here is a better question.

    What is the probability that given a really shitty bill that will do way more harm to the country in every way than it will ever do good, that congress will do the right thing and vote against its passage? 0% or .000001%?

  • johnl||

    50% is not such a bad answer. It's 50% to come up the same way both times. Maybe they misunderstood the question. Of course, many people think that 50% is the right answer to every question.

  • Hyperion||

    50% producers for revenue, 50% takers and assured voters. Sounds like the winning formula for the DNC.

  • Trespassers W||

    So three out of four Labour MPs misunderstood the question? Is that really more plausible?

  • ||

    There's an anecdote from WWII about this old Soviet woman who, at the outset of the war, was asked by a reporter what she thought the odds were that the Germans would invade Moscow.

    "50%", she replied.

    "That high a chance?" asked the reporter.

    "Well, either they will, or they won't.", retorted the woman.

  • johnl||

    This is an example. It's just this error that makes the Monte Hall problem so easy to get wrong.

  • Doctor Whom||

    Perhaps most depressingly is how confident MPs said they were in their numerical skills, with 76 percent of Tories and 72 percent of Labour MPs saying that they were confident when dealing with numbers.

    It's Team Dunning vs. Team Kruger.

  • Killazontherun||

    According to the Koran, even God couldn't get basic math problems correct. What do you expect of a mere law maker?

  • johnl||

    Makes you wonder what those "other" were. Maybe "I would have pocketed the coin before anyone had the chance to flip it a second time".

  • Sidd Finch||

  • misthiocracy||

    I would have gotten it wrong.

    Should I be disqualified from elected office?

  • ||

    ...yes.

  • johnl||

    What wrong answer would you have given?

  • ||

    Many politicians are bad at math, leftist politicians more than right-wingers. They are, unfortunately, actually representative representatives.

    My GF got the question wrong, too. 50% was her answer.

  • johnl||

    I would guess that a person getting a wrong answer will go with 50% about 50% of the time. Which is such a waste, given all the wrong answers available.

  • Rights-Minimalist Autocrat||

    Yeah, I'd like to hear something creative like 4.817%

  • johnl||

    People answered 15%, 40%, and 75%. The last is just 1 - the right answer. But the other two are as original as 4.817%. A vector answer would be even more original.

  • Franklin Harris||

    What of the Lib Dems? Are they in between as usual?

    Obligatory link to an economically related scene from "The Thick of It": http://youtu.be/DeAEiSSDPNA

  • cavalier973||

    How many the MP's that got the answer wrong requested instruction on why their answer was wrong, and what one did to get the correct answer? Being ignorant of something is not so bad as remaining so when presented with an opportunity to rectify the situation.

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