Scandal! The International Tiddlywinks Council (or the ITC) has been charged wit

Question

Scandal! The International Tiddlywinks Council (or the ITC) has been charged with taking bribes in order to choose where the Tiddlywinks World Cup should be held. The eligible host cities are: Sao Paulo (in Brazil); Beijing, Guangzhou, Shanghai, Shenzhen (in China); Kinshasa (in DR Congo); Cairo (in Egypt); London (in England); Delhi, Mumbai (in India); Jakarta (in Indonesia); Tokyo (in Japan); Mexico City (in Mexico); Lagos (in Nigeria); Karachi, Lahore (in Pakistan); Lima (in Peru); Moscow (in Russia); Seoul (in South Korea); Istanbul (in Turkey).1 The ITC claims it chooses the city randomly, with an equal likelihood for each. For the last three World Cups, though, the event was held in Pakistan.

The Questions: Counting

How many eligible cities are in each country? How many cities are in each continent?

In how many ways could the cities be chosen for three World Cups?

In how many ways could the countries be chosen for three World Cups?

The Questions: Probability

Assuming an equal likelihood for each city, find the probability for each country that a World Cup will be in that country. Are all countries equally likely?

Find the probability for each continent that a World Cup will be in that continent.

Find the probability that a city not in China will be chosen for a World Cup.

Find the probability that, for three World Cups in a row, the World Cup is not held in China.

Find the probability that a city in Asia will be chosen for a World Cup.

Find the probability that, for three World Cups in a row, the World Cup is held in Asia.

Find the probability that, for three World Cups in a row, the World Cup is held in Pakistan.

The Questions: Interpretation and Exploration

Given the probability you found above, how strong do you think the evidence is against the ITC? Do you think it is more reasonable to believe that the result was truly random, or that the ITC is fixing the results? Give your reasons behind your choice.

Think of some other ways the decision could be made to avoid any appearance of favoritism by the ITC. What other advantages and drawbacks do these ways have?

Explanation / Answer

1. Eligible cities are in each country: China - 4, India - 2, Brazil -1, Pakistan -2, Indonesia -1, Japan -1, Nigeria -1, England -1, Egypt -1, Peru-1, Russia-1, South Korea-1, DR Congo-1, Turkey-1,Mexico-1.

Cities are in each continent: Asia - 11, Europe - 3, Africa - 3, South America - 3.

2. (1/20)^3

3.(1/15)^3

4. No. India, Pakistan - 1/10; China - 1/5; Rest - 1/20.

5.Asia - 11/20; Rest - 3/20.

6.City Not in China = 1 - (1/5) = 4/5.

7. Country not China = 1-(1/15)^3.

8.City In asia = 11/20.

9.3 world cups in Asia = (11/20)^3.

10. Pakistan - (1/10)^3

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.