Thursday, 10 November 2016

Quibans 48: Trump and the pollsters

From The Guardian:

This was a good starting point for a Quibans.

First of all, if there was a “15% chance” and that happened, it doesn’t necessarily mean the prediction was wrong – just that something less likely did occur.

I didn’t understand that comparison that was given here.

Questions:
  1. What does this mean:  15% chance is roughly the same as rolling a six if you have two dice.
  2. Can you come up with a better comparison that uses coins, dice, cards, etc.

Answers:
  1. It might mean

  • Getting a sum of 6 when you roll two dice.
  • Getting exactly one six if you roll two dice.
  • Getting one or more sixes if you roll two dice
A probability table might be useful here:


This shows the total of the two dice.  There is therefore a probability of 5/36 of getting a total of 6, which is about 13.9%

This table shows (in yellow) the ones where exactly one die shows 6.  10/36 = 27.8%















If we include a double-six too then that rises to 30.6%

The first of these (a total of 6) is nearest to 15%.  If it had said “getting 8 when you roll two dice” the probability would have been the same but the ambiguity would have been removed.

A better comparison
The probability of getting a 6 on a six-sided die is 1/6, which is 16.7%.  This is so much clear but is only a tiny bit less accurate than the suggestion in the article, so this is arguably better.
The probability of getting an Ace or a King from a pack of cards is 8/52 = 15.4%, which is very close and is also easy to understand.


[Other issues related to this also appear on my blog.  Find it here.]

Source:


Friday, 4 November 2016

Quibans 47: Shortest flights

From the Daily Telegraph:

The world's 10 shortest flights

A list of the world's 10 shortest regular commercial flights contains an international service for the first time, thanks to a 13-mile, eight-minute route between Switzerland and Germany that launched today.
In more excitement for fans of ludicrously brief forays into the sky, this week the world’s largest commercial aircraft - the Airbus A380 - was handed a regular outing on its shortest ever flight - a mere 235-mile jaunt between Doha and Dubai. Emirates, the airline behind the route, regularly uses the behemoth "superjumbos" on 8,000-mile odysseys, but instead thought it could be put to good use nipping between the two Middle Eastern cities. The journey could conceivably be made 40 times before the need to refuel.
But what of the rest of the world’s tiniest hops?
The competition to become a member of this club is not as fierce as it is at the other end of the scale, where airlines battle to out-fly each other to the longest non-stop schlep, but is nevertheless one of intrigue.
Topping the table is the wonderfully unconventional two-minute Loganair service between Westray and Papa Westray in Scotland’s Orkney Islands, which are separated by just 1.7 miles of land and sea. It can be completed in as little as 47 seconds, depending on the direction of the wind, and welcomed its millionth passenger this week. 
Featuring more obscure airlines, such as Pacific Wings and Guam’s finest carrier, Freedom Air, read on to find out about 10 flights that cover a total of just 91.5 miles - less than the distance between London and Bristol.






What a great story!  What can we work out?

Questions:
  1. What is the average speed for each journey? (We could do this for the new route and also for the Orkney flight.)
  2. How far can the A380 fly without needing to refuel?
  3. What sort of correlation is there between the length of the flight in miles and the length in minutes?

Here is the data from the image, shown in a spreadsheet:

Distance
Duration
miles
mins
10
Cayman Brac
14 miles
10 mins
14
10
9
Friedrichshafen
13 miles
20 mins
13
20
8
Karpathos
12 miles
5 mins
12
5
7
Papeete
11 miles
15 mins
11
15
6
Saipan
10.8 miles
10 mins
10.8
10
5
Connemara
10.4 miles
6 mins
10.4
6
4
Hoolehua
8.8 miles
10 mins
8.8
10
3
Minami-Daito
7 miles
15 mins
7
15
2
Caye Chapel
2.4 miles
2 mins
2.4
2
1
Westray
1.7 miles
2 mins
1.7
2

Answers:
13 miles in 8 minutes means 1.625 miles in 1 minute and 97.5 mph.
1.7 miles in 47 seconds means 0.036170213 miles in 1 second and (multiply by 3600)
130mph.
235 x 40 = 9400 miles.  But this might not be accurate, because it will presumably depend on wind-direction and wind-speed, there will be 40 take-offs and 40 landings rather than just one of each, which might use a different amount of fuel.  Presumably there are also rules about having to have a certain amount of fuel in reserve in case of bad-weather diversions, etc.
The pmcc is 0.58, which shows a weak positive correlation.  We could also draw a scattergraph.



Quibans 71: I’d walk a million miles for one of your goals

Apparently (thanks to Scott for the heads-up), Scottish football fans sing “I’d walk a million miles for one of your goals”.  [ Link ]   ...