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In ‘crossword format’

Quick

The government just announced a reduction in VAT from 17.5% to 15%. How much money do you save per £100?

Cryptic

You’re at a magic show. The magician asks you to shuffle the cards (a normal 52 card deck) and hand them back to you. He asks a member of the audience to name a card. The audience member names the Ace of Spades. The magician draws a single card out of the deck. What is the chance (odds?) of the card drawn being the card named?


EOD: Answer Update (after 9 comments)

Quick

The papers/press/media have all been reporting that with a 2.5% reduction in VAT you’ll only be saving £2.50 in every £100 by working out the complex equation of “What’s 2.5% of 100?”. Of course this is clearly wrong.

In £100 payment inclusive 17.5% tax you’re paying £14.89 tax such that the item value would have been £85.11

A 15% tax on £85.11 would result in £12.77 tax.

£14.89 - £12.77 = £2.12 savings.

Of course as Nigel points out, there is actually a more complex answer here too (based on my question), and that even for a specific right answer, there can be multiple right answers.

Also everyone has been writing in to letters pages commenting how pointless the reduction is, as £2.50 is not a lot of money. Which proves my point that most people are idiots who don’t understand anything. I wont explain here why a 2.5% decrease is significant, just to say image how people would have reacted had VAT gone UP by 2.5%.

Cryptic

The question really is about how we evaluate risk. And how we consider the factors involved. There is no real right answer here, the right answer is in how we explain the answer. Of course some answers are more right than others.

Marc was the most correct here, or put another way, had a most correct answer.

A simple way of looking at it is like this

  • The random chance of pulling a specific card out of a deck is 1 in 52
  • However we know we are at magic show and we know a magician probably knows what we are doing so we could consider the odds are then really 1 in 1.
  • However looking at the factors again, we know a magician probably is going to not pull the card out the first time to build suspense, so we could say the odds are 0 in 1.
  • Or we can factor together different tricks (as Marc did) and calculate even more precise odds.

So those are the two answers (or two of the answers) to today’s Friday Pop Quiz questions. I’ll be honest I stole the questions from the BBC R4 More or Less podcast. If you want to listen to more detail you can watch it on iPlayer or download here

I quite liked pop quiz Friday. More for the debate and interesting perspectives (including @Jack (2)’s). I might do this every week. If I can think of enough interesting questions.

9 Comments

12 Dec, '08 10:03 AM

1. Will

£2.13 I think?

To the cryptic: if the magician is aiming to pick it out, probably 1 - if they’re planning to get it wrong, 0. And if it’s just random, 1 in 52.

  1. Charles Dickens
  2. The Polish–Swedish War of 1600–1611
  1. £2.12 I think?

  2. No doubt this will trigger QI-style WOOGA WOOGA YOU ARE WRONG alerts, but I’m guessing 1 in 52?

12 Dec, '08 10:44 AM

4. Marc

1) If you are looking at an item that cost £100 after VAT then it will £2.127 cheaper with the new rate.

2) My guess would be somewhere between evens to 1 in 5. Let’s call it 2 in 7.

12 Dec, '08 10:49 AM

5. Adrian

@Marc (4), Can you explain your thinking for point 2?

(unless you want to wait till other people have answered a bit, and see what people are saying, which is cool too)

12 Dec, '08 10:51 AM

6. Marc

Correction: £2.128

Although if you were looking to spend your whole £100 then you can afford things that are £1.850 more expensive pre-VAT.

12 Dec, '08 12:06 PM

7. Marc

Spoiler

It’s a bit plucked out of the air on the probability calculation front but considering it’s a magician then I assume the trick is to reveal the card. A straight forward card trick would reveal the card straight away which means it’s an even chance. But then I thought about one of my card tricks and there’s three iterations before the reveal. And I can think of a trick that goes through five iterations before the selected card is revealed.

Assuming there are card tricks that present the reveal instantly and after 5 iterations. We will discount tricks with more iterations as too few to be statistically relevant as they approach interminably long and tedious tricks.

So if the tricks with 1 to 5 iterations were evenly distributed there would be 1 in 5 chance that it would be your card.

But as I plucked my number out of the air I’m going to prove it. In fact I actually know that the distribution of card tricks looks like this:

Reveals | # of Tricks*
      1 |         240 
      2 |         180
      3 |         210
      4 |          90
      5 |         120
  Total:          840

So for immediate reveals: 240/840 = 28.57% = 2/7.

* Officially recognised reveal card tricks - Magic Circle Census 2003

12 Dec, '08 12:16 PM

8. Nigel

  1. There’s actually no simple answer to this.

    The government is funding this VAT cut with extra borrowing, which will need to be paid off in the future by increased taxes. So how much you “save” (or, potentially “lose”) depends on the combination of your future overall tax burden (in turn dependent on the shape of future tax policy to pay off the extra borrowing) and your current consumption (of products on which you pay VAT).

  2. I don’t think there’s much to add to Marc’s explanation here.

12 Dec, '08 3:15 PM

9. Matt

Quick answer: Not much.

Cryptic answer: The chance is high, but the odds are low.

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