Question

Consider a game show where an adversary chooses two distinct numbers $a, b \in [0, 100]$ such that $a \neq b$. After the adversary has chosen $a$ and $b$, he cannot change them. Your aim is to choose the largest of the two numbers. You can ask the adversary to reveal the value of one of the two numbers, after which, you have to make your choice. Devise a strategy that succeeds with probability $> 1/2$, even when the adversary knows your strategy.

          Consider a game show where an adversary chooses two distinct numbers $a, b \in [0, 100]$ such that
$a \neq b$. After the adversary has chosen $a$ and $b$, he cannot change them. Your aim is to choose the
largest of the two numbers. You can ask the adversary to reveal the value of one of the two numbers,
after which, you have to make your choice. Devise a strategy that succeeds with probability $> 1/2$,
even when the adversary knows your strategy.

Consider a game show where an adversary chooses two distinct numbers a, b ∈ [0, 100] such that
a ≠ b. After the adversary has chosen a and b, he cannot change them. Your aim is to choose the
largest of the two numbers. You can ask the adversary to reveal the value of one of the two numbers,
after which, you have to make your choice. Devise a strategy that succeeds with probability > 1/2,
even when the adversary knows your strategy.

Added by Brian P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert James Kiss

04/03/2023

Step 1

Since we want to choose the largest number, it makes sense to ask the adversary to reveal the number that is more likely to be the larger one. Show more…

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Consider a game show where an adversary chooses two distinct numbers a,b E [0,100] such that a b. After the adversary has chosen a and b, he cannot change them. Your aim is to choose the largest of the two numbers. You can ask the adversary to reveal the value of one of the two numbers. after which, you have to make your choice. Devise a strategy that succeeds with probability > 1/2 even when the adversary knows your strategy.