Proportional Probability Dice

Probability Level 1

I have a special 6-sided dice such that

The probability of rolling a 2 is twice the probability of rolling a 1,
the probability of rolling a 3 is thrice the probability of rolling a 1,
the probability of rolling a 4 is quadruple the probability of rolling a 1,
the probability of rolling a 5 is quintuple the probability of rolling a 1, and
the probability of rolling a 6 is hextuple the probability of rolling a 1.

What is the probability of rolling a 1?

Clarification : Each face of the dice is labelled with a distinct integer in the interval 1 to 6 (inclusive).

\frac1{1+2+3+4}

\frac1{1+2+3+4+5}

\frac1{1+2+3+4+5+6}

\frac1{1+2+3+4+5+6+7}

1 solution

Akhil Bansal
Apr 29, 2016

Relevant wiki: Probability - Rule of Sum

Let the probability of rolling 1 is $\color{#3D99F6}{\text{k}}$

Then, probability if rolling 2 is $2\color{#3D99F6}{\text{k}}$ .
Probability of rolling 3 is $3\color{#3D99F6}{\text{k}}$ .
And similarly others.

sum of probability of rolling all numbers = 1 $\color{#3D99F6}{\text{k}} + 2\color{#3D99F6}{\text{k}} + \ldots + 6\color{#3D99F6}{\text{k}} = 1$

$\color{#3D99F6}{\text{k}} = \dfrac{1}{1+2+\ldots+6}$

Proportional Probability Dice

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