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.

a) This is a fair method in terms of probability.
b) This is not a fair method in terms of probability.
c) Both of the above
d) None of the above

Answer 1

The draft lottery system is considered a fair method in terms of probability because it ensures that every individual has an equal chance of being chosen, similar to the simple random sampling method.

Step-by-step explanation:

The method described for deciding who must enlist in the military seems to be a fair method in terms of probability. Every date of the year is given the same chance of being selected since they are loaded into identical capsules and drawn randomly. This ensures that each high school student born on any day of the year has the same chance to be drafted.

This method can be likened to simple random sampling where each member of the population has an equally likely chance of being chosen. For example, tossing a coin is a fair method to decide who goes first in a competition because there is an equal probability of landing on heads or tails. Similarly, in the draft lottery system, if all procedures are followed correctly, there is an equal probability for every potential draftee to be chosen, assuming there are no biases in the system, and that every birth date is represented once and only once in the capsule pool.

The description aligns with a fair way to conduct a lottery as mentioned in the provided reference, where a completely random method is used to select individuals, maintaining equal chances at every stage of the sampling process.