Unfair Game

Probability Level 3

You are given magnetized pair of dice, which have the probability of turning up 6-face five times more than other faces. (Other faces are still randomly distributed.)

What is the expected value of points when tossing these cheating dice?


The answer is 9.

Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

By increasing the probability of 6-face to be 5 times more than other faces, the distribution will be 5 10 \dfrac{5}{10} for 6-face and 1 10 \dfrac{1}{10} for other faces; 1 = 0.5 + 0.1 × 5 1 = 0.5 + 0.1\times 5

Expected value for 2 dice = 2 ( 1 + 2 + 3 + 4 + 5 10 + 6 2 ) = 9 2(\dfrac{1+2+3+4+5}{10} + \dfrac{6}{2})= 9 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Lol I wondered what I was doing wrong... Turns out nothing in my thinking but everything when calculating. I used 0.5 x 6 + 0.2(stupid of course) 15.

Peter van der Linden - 4 years, 6 months ago

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It surely exceeded the number of both dice combined. Lol...

Worranat Pakornrat - 4 years, 6 months ago

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