# Denmark Kangaroo Orange Trick & Mathematical vs Real Life Probability

A Brain Teaser which is very popular on net goes as below:

1. pick a number between 2 and 9

2. multiply it by 9

3. add the two digits in the new number not counting their place values

4. minus 5 from that answer

5. every number stands for a letter 1 – A, 2 – B, 3 – C, find your letter

6. think of a country that starts with that letter

7. take the last letter of that country and think of an animal

8. take the last letter of that animal and think of a fruit

**Now let’s analyze the problem step by step:**

First part: Guess a number and Multiply it with 9, then add its digits and reduce 5 from it.

This part is just a simple distraction to make you feel you are doing something complex. As many of you may know multiplying any number by 9 and adding its digits till you get a single digit will always result in 9.

(visit http://mathforum.org/library/drmath/view/67061.html for more information)

Now when you remove 5 from 9, you are always left with 4 and Fourth letter of alphabet is “D”,

As you may know:

(1) You have four countries starting with “D”

(a) Denmark

(b) Djibouti

(c) Dominica

(d) Dominican Republic

Hence Mathematically you will agree that you have 1/4 chances of selecting Denmark

(2) Now If you have selected Denmark then what is the chance that you will select Kangaroo in the next round?

Well you have following choices

(a) Kangaroo

(b) Kaffir cat

(c) Kafue flats lechwe

(d) Kelp gull

(e) Killer whale

(f) Kinkajou

(g) Kirk’s dik dik

(h) Klipspringer

(i) Koala

(j) Komodo dragon

(k) Kongoni

(l) Kudu

So you have 12 choice (including killer whale where I am giving benefit of doubt)

This means that Mathematically you have 1/12 Chance of Selecting Kangaroo.

(3) What is the probability that you will choose Orange once you choose Kangaroo

Now This is relatively easy, you have only two choices it can be either Olive or Orange.

Hence again Mathematically Speaking you have 1/2 chances of selecting Oranges.

To conclude, Mathematically speaking your chances to select Denmark –> Kangaroo –> Oranges is exactly 1/4 x 1/12 x 1/2 = 1/96 or just above 1%.

**Now lets look at reality:
**When we search Denmark, Kangaroo & Oranges in Word Popularity Index http://www.wordcount.org/main.php or Number of result count from Google Search with relative ranking among its peers something amazing happens 🙂

(1) Word –> Rank

Denmark –> 5770

Djibouti –> 19993

Dominica –> 37580

Dominican Republic –> Not Ranked

This implies that almost 100% will select Denmark but Let’s give benefit of doubt again and make it 95%.

(2) Word –> Rank

Kangaroo –> 27219

Kaffir cat –> 76576

Kafue flats lechwe –> Not Ranked

Kelp gull –> 55362

Killer whale –> NA

Kinkajou –> Not Ranked

Kirk’s dik dik –> Not Ranked

Klipspringer –> Not Ranked

Koala –> 69579

Komodo dragon –> 76472

Kongoni –> Not Ranked

Kudu –> 75640

Which again implies that 95% + would have chosen Kangaroo

Now for Last one:

(3) Word –> Rank

Orange –> 3442

Olive –> 7501

However one need to consider that Orange is more likely to come in everyone’s mind as its most commonly associated with Fruit in daily world and not the olive. However by giving benefit of doubt again we take 95%+ chance of selecting Orange.

To conclude, in reality your chances to select Denmark –> Kangaroo –> Oranges is about 95% ^ 3 or approx 86%+

Amazing isn’t it? This is the best example how Mathematical probability can just prove terribly wrong in real life.

If you like this post, share with your Nerd friends to enlighten them 🙂

You can browse references below:

|| Word popularity Index || Sum of Digits of Multiple of 9 || Countries Starting with ‘D’ || Animal Names starting with ‘K’ || Fruits Name starting with ‘O’||