The Data Show the Total Number of Medals (Gold, Silver $$\begin{array} { l l l l l l l l l } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29\end{array}$$

question 167

Essay

The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. $$\begin{array} { l l l l l l l l l } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29\end{array}$$ Suppose that one of the countries represented is selected at random and the total number of medals won by that country is noted. What is the probability that the country won at least 25 medals given that the country did not win fewer than 10 medals?

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Definitions:

Pareto Optimal

A state of allocation of resources from which it is impossible to reallocate to make any one individual better off without making at least one individual worse off.

Competitive Equilibrium

A state in markets where supply equals demand, and no participant has an incentive to change their behavior.

Strawberries

A sweet, red, heart-shaped fruit that is widely appreciated for its characteristic aroma, bright red color, juicy texture, and sweetness.

Champagne

A sparkling wine produced from grapes grown in the Champagne region of France, known for its production method and prestigious reputation.