Predictive Survey Results

You don't find many grey elephants in Denmark do you?

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 Results

• Survey began: 7am (GMT) on 20th November 2014
• So far 5013 survey entries have been received in which the calculations were correct.

• 69% 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.

• 67% of those who chose Denmark then chose an elephant.
• 9% of those who chose Denmark then chose an emu.
• 11% of those who chose Denmark then chose an eagle.
• 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.
• 3% of those who chose Denmark then chose an echidna.
• 1% of those who chose Denmark then chose an ermine.

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

Chosen Number	Frequency	Percentage
2	1528	30%
3	489	10%
4	400	8%
5	603	12%
6	209	4%
7	399	8%
8	202	4%
9	251	5%
10	158	3%
11	62	1%
12	65	1%
13	31	1%
14	25	0%
15	21	0%
16	10	0%
17	28	1%
18	18	0%
19	12	0%
20		0%

Here is the short URL of the survey that you could sent 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.