Question

Determine whether the following method is a fair way (in terms of probability) to decide who must enlist in the military: During a war the U.S. government institutes a draft lottery in which each of the dates of the year (including Feb 29)) are loaded into identical capsules. The date in each capsule is printed randomly and packed into the capsule by a computer, and then all capsules are loaded into a barrel in no particular order, stirred, and poured into another barrel. The numbers are then drawn from the second barrel and individuals with birth dates corresponding to the date drawn from the barrel are drafted into the military. Is this a fair method in terms of probability?

a) This is a fair method in terms of probability - Assuming that all dates are equally likely to be drawn and individuals are equally likely to be born on any given date, the method is fair.

b) This is not a fair method in terms of probability - If certain dates or months are more likely to be drawn due to biases in the process, or if certain birth dates are overrepresented, the method may not be fair.

c) Not enough information - Without specific details about the randomness of the drawing process and the distribution of birth dates, it's challenging to definitively determine the fairness of the method.

d) None of the above

Answer 1

The fairness of the draft lottery depends on the randomness of the date assignment and selection process, as well as the distribution of individuals' birth dates. Without specific details about the process or the birth date distribution, it's difficult to definitively assess fairness.

Step-by-step explanation:

To determine whether the draft lottery described is a fair method in terms of probability, we must consider whether each individual has an equally likely chance of being chosen. This process involves each date of the year being randomly printed and loaded into identical capsules, which are then mixed and drawn from a barrel. The key criteria for fairness include the randomness of the date assignments to capsules, the thoroughness of the mixing process, and the randomness of the draw. If all these conditions are met and each individual has an equal chance of being born on any given date, then option a. This is a fair method in terms of probability, would be correct.

However, if there is bias in the process, such as certain dates being more likely to be drawn, or if there is an unequal representation of birth dates, then the method could be unfair, leading us to consider option b. This is not a fair method in terms of probability. Nevertheless, without further information about the actual randomness of the drawing process or the distribution of birth dates, it is difficult to definitively conclude, possibly suggesting option c. Not enough information.

As an example, consider the scenario where a die is biased because of differences in weight due to the number of holes for each number. Gambling casinos take great pains to eliminate such biases in dice to ensure fairness. Similarly, in a draft lottery, measures would need to be taken to ensure there is no bias in the selection process.