Question

Two loaded dice used, such that the probabilities of 1,2,3,4,5,6 are 1-x/6, 1+2x, 1-x/6, 1+x/6, 1-2x/6, 1+x/6 respectively. Find x

Answer 1

Solution:

Using $\Sigma p_i=1$

$(\dfrac{x}{1}-\dfrac{x}{6})+(\dfrac{1+2x}{6})+(x-\dfrac{1}{6})+(\dfrac{1+x}{6})+(\dfrac{1-2x}{6})+(\dfrac{1+x}{6})=1 \\\Rightarrow x=\dfrac3{13}$