select the correct answer. which of these sortition methods can be used to select a person for a certain…

select the correct answer. which of these sortition methods can be used to select a person for a certain task from among 24 candidates? a. throw 2 dice. assign a combination (for example 5 - 6) to each candidate. b. flip a coin 5 times. assign a sequence (for example h - t - h - h - t) to each candidate. c. roll a dice 1 time and flip a coin 2 times. assign a sequence (for example 4 - h - t) to each candidate. d. flip a coin and roll 2 dice. assign a sequence (for example h - 3 - 4) to each candidate.

select the correct answer. which of these sortition methods can be used to select a person for a certain task from among 24 candidates? a. throw 2 dice. assign a combination (for example 5 - 6) to each candidate. b. flip a coin 5 times. assign a sequence (for example h - t - h - h - t) to each candidate. c. roll a dice 1 time and flip a coin 2 times. assign a sequence (for example 4 - h - t) to each candidate. d. flip a coin and roll 2 dice. assign a sequence (for example h - 3 - 4) to each candidate.

Answer

Explanation:

Step1: Calculate number of outcomes for option A

When throwing 2 dice, the number of possible combinations is (6\times6 = 36). But some combinations are duplicates (e.g., 1 - 2 and 2 - 1 are different throws but may be considered the same for assignment in a non - ordered sense). The non - duplicate combinations are (\frac{6\times(6 + 1)}{2}=21<24), so it's not sufficient.

Step2: Calculate number of outcomes for option B

When flipping a coin 5 times, the number of possible sequences is (2^5=32>24). Each sequence is unique, and we can assign one sequence to each of the 24 candidates.

Step3: Calculate number of outcomes for option C

Rolling a dice 1 time gives 6 outcomes and flipping a coin 2 times gives (2\times2 = 4) outcomes. The total number of sequences is (6\times4=24). But the probability distribution may not be as uniform as in the coin - flip case.

Step4: Calculate number of outcomes for option D

Flipping a coin gives 2 outcomes and rolling 2 dice gives (6\times6 = 36) outcomes. The total number of sequences is (2\times36 = 72). While it has enough outcomes, it's more complex than needed.

Answer:

B. Flip a coin 5 times. Assign a sequence (for example H - T - H - H - T) to each candidate.