The activity which prompted this survey is on our Mathemagic page. The instructions below are intended to be read out by the "magician":

- Think of a number
- Multiply it by nine
- Add the digits of your answer together
- Subtract five
- If A=1, B=2, C=3 etc what letter is represented by the number you are thinking of now?
- Think of a country beginning with that letter
- Think of an animal beginning with the second letter of that country
- What is the colour of that animal?

The magician then says "*"There aren't many grey elephants living in Denmark are there?"*"

Virtually everyone in the room will have thought of Denmark as their country
and as elephant as their animal. Is this magic?

You could investigate the probability of this happening. Having first
satisfied yourself that everyone will arrive at the letter D independently
of their starting number. How many countries are there starting with D?

How many animals beginning with E? Of all the animals beginning with E how
likely is a person to choose elephant? This survey attempts to answer this
question.

Can you make up for yourself a similar trick (but
not using Elephants from Denmark).

Finally a demonstration of tree diagrams can be used to explain the
probabilities of these tricks working.

- Survey began: 7am (GMT) on 20th November 2014
- So far 3704 survey entries have been received in which the calculations were correct.

- 70% of those entries had chosen Denmark.
- 7% of those entries had chosen Dominican Republic.
- 5% of those entries had chosen Djibouti.
- 2% of those entries had chosen Dubai (even though Dubai is not a country).
- 4% of those entries had chosen Dominica.

- 69% of those who chose Denmark then chose an elephant.
- 9% of those who chose Denmark then chose an eagle.
- 9% of those who chose Denmark then chose an emu.
- 4% of those who chose Denmark then chose an eel.
- 1% of those who chose Denmark then chose an earthworm.
- 2% of those who chose Denmark then chose an elk.
- 2% of those who chose Denmark then chose an echidna.
- 1% of those who chose Denmark then chose an ermine.

Denmark

Dominican Republic

Djibouti

Dubai (even though Dubai is not a country)

Others

Elephant

Eagle

Emu

Eel

Others

70%

7%

5%

2%

16%

69%

9%

9%

4%

9%

The following table shows how popular the starting numbers were. Numbers greater than 20 are not shown.

Chosen Number | Frequency | Percentage |
---|---|---|

2 | 1103 | 30% |

3 | 367 | 10% |

4 | 289 | 8% |

5 | 457 | 12% |

6 | 163 | 4% |

7 | 285 | 8% |

8 | 143 | 4% |

9 | 194 | 5% |

10 | 125 | 3% |

11 | 45 | 1% |

12 | 52 | 1% |

13 | 26 | 1% |

14 | 12 | 0% |

15 | 13 | 0% |

16 | 8 | 0% |

17 | 20 | 1% |

18 | 14 | 0% |

19 | 7 | 0% |

20 | 32 | 1% |

How do you spell that colour? The colour of the elephant!

Grey | 84% |

Gray | 16% |

Here is the short URL of the survey that you could send to other people: Transum.org/go/?to=Survey

The motivation for conducting this data collecting exercise is an email from a TV researcher saying that John Stossel would like to use the tree diagram for his show on Fox Business Network to be broadcast at 9pm on 4th December 2014. The probabilities on the original diagram were made-up numbers for illustration only and the request to use the diagram prompted Transum to collect real data and update the diagram.

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

Mitchell, US

Tuesday, November 25, 2014

"I took the survey and ended up with Denmark and chose an emu but then felt not so smart because I really didn't know if an emu was grey or white. So I switched to elephant and found out I was with the majority of others who chose elephant. I wonder how many of those switched from emu to elephant for the same reason. Does the model predict that?"