In World War II, during the summer of 1944 , the Russians were driving back the Germans. Stalin wanted to launch a fierce attack at one of three spots in western Russia: the north, the south, or the center. He also wanted to be completely unpredictable in his decision.

Which of the following would have been fair methods for deciding where to attack?
(Consider a system to be fair when the probabilities of each event are equal.)

Choose all answers that apply:
A Stalin asks one of his officers to choose the place of attack.
B Stalin rolls three 6 -sided dice. If all 3 numbers are different, he attacks in the north. If all 3 numbers are the same, he attacks in the south. If 2 numbers are the same and the other is different, he attacks in the center.

C Stalin flips 2 coins. If the first coin is heads, he attacks in the north and ignores the second coin; if it is tails he rules out attacking the north and moves on to the second coin. If he gets to the second coin and it is heads, he attacks in the center; if it is tails he attacks in the south.

D Stalin writes down the numbers 1,2 , or 3 on pieces of paper. He asks his leading officer to choose one of the pieces from a hat. If the officer chooses 1 , they attack in the north. If the officer chooses 2 , they attack in the center. If the officer chooses 3 , they attack in the south.

Question

In World War II, during the summer of 1944 , the Russians were driving back the Germans. Stalin wanted to launch a fierce attack at one of three spots in western Russia: the north, the south, or the center. He also wanted to be completely unpredictable in his decision.

Which of the following would have been fair methods for deciding where to attack?
(Consider a system to be fair when the probabilities of each event are equal.)

Choose all answers that apply:
A Stalin asks one of his officers to choose the place of attack.
B Stalin rolls three 6 -sided dice. If all 3 numbers are different, he attacks in the north. If all 3 numbers are the same, he attacks in the south. If 2 numbers are the same and the other is different, he attacks in the center.

C Stalin flips 2 coins. If the first coin is heads, he attacks in the north and ignores the second coin; if it is tails he rules out attacking the north and moves on to the second coin. If he gets to the second coin and it is heads, he attacks in the center; if it is tails he attacks in the south.

D Stalin writes down the numbers 1,2 , or 3 on pieces of paper. He asks his leading officer to choose one of the pieces from a hat. If the officer chooses 1 , they attack in the north. If the officer chooses 2 , they attack in the center. If the officer chooses 3 , they attack in the south.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Evaluate the fairness of Option A: Stalin asks one of his officers to choose the place of attack. ‖ ‖ step 2 ⋮ This method's fairness cannot be quantified without knowing the officer's decision-making process. ‖ ‖ step 3 ⋮ Evaluate the fairness of Option B: Stalin rolls three 6-sided dice and decides based on the outcome. ‖ ‖ step 4 ⋮ Calculate the probability of each attack location. For the north, all three dice must show different numbers. ‖ ‖ step 5 ⋮ The probability of rolling three different numbers on three 6-sided dice is not equal to the probability of rolling three of the same or two of the same and one different. ‖ ‖ step 6 ⋮ Evaluate the fairness of Option C: Stalin flips 2 coins to decide the attack location. ‖ ‖ step 7 ⋮ Calculate the probability of each attack location. The first coin determines if the north is chosen or not. ‖ ‖ step 8 ⋮ The probability of choosing the north is 1/2, and the probability of choosing between the center and the south is also 1/2. ‖ ‖ step 9 ⋮ Since the second coin is only used if the first is tails, the probabilities for the center and south are each 1/4. ‖ ‖ step 10 ⋮ Evaluate the fairness of Option D: Stalin uses pieces of paper numbered 1 to 3. ‖ ‖ step 11 ⋮ Calculate the probability of each attack location. Each piece of paper has an equal chance of being chosen. ‖ ‖ step 12 ⋮ The probability of choosing any of the three locations is 1/3, which is fair. ‖ ∻Answer∻ ⚹ Option D is the fair method for deciding where to attack. ⚹ ∻Key Concept∻ ⚹Fairness in Probability⚹ ∻Explanation∻ ⚹A method is considered fair if it provides equal probabilities for all possible outcomes. In this context, each attack location should have an equal chance of being chosen. Option D satisfies this condition.⚹◊What is the probability of Stalin choosing the attack location in the north if he rolls three 6-sided dice according to Option B?⍭ Generate me a similar question◊

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