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:


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