Death Deal

Probability Level 3

The Grim Reaper came to face you before your destined ending and slyly challenged you to guess whether your remaining life span would be in odd or even years.

Then the Reaper offered you a death deal:

If you guessed right, your remaining life span would be doubled.

If you guessed wrong, the life span would be halved.

Should you have taken this bet if you wished to live longer?

No, less life span can be expected Not enough information Yes, more life span can be expected Not really, zero life span is expected

2 solutions

Worranat Pakornrat
Jan 14, 2017

Let $x$ be the remaining life span. By guessing odd or even, there is a 50:50 chance to get it right. Then by getting it right, more $x$ years would be granted while by getting it wrong, $\dfrac{x}{2}$ years would be lost.

Then the expected value of life span with this bet = $(+x)(\dfrac{1}{2}) + (\dfrac{-x}{2})(\dfrac{1}{2}) = \dfrac{x}{4}$ .

Therefore, more life span could be expected from this bet, and in theory, it is worth a deal (for daring persons, of course).

Chew-Seong Cheong
Jul 25, 2017

Let your remaining lifespan be $L$ . It has the same probability or $p=q=\frac 12$ of ending in odd or even year.

The expected value of your lifespan if you take the bet would be $p(2L)+(1-p)\dfrac L2=\dfrac 12\times 2L+\dfrac 12\times \dfrac L2 = 1\frac14l$ . Your lifespan is expected to be extended by a quarter.

Yes, more lifespan can be expected.

Death Deal

2 solutions

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