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:**

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

**Answers:**

- 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

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: