Suppose C={1,2,3) and two compound lotteries are defined as follows L₁ ={l₁,l₂,l_(3),(1)/(3),(1)/(3),(1)/(3)}, and L₂={l₄ ,l₅,(1)/(2),(1)/(2)}, with l₁=(1,0,0),l₂=(0,1,0), and l₅=(q,1-q,0).
Find the value of p and q such that L₁ and L₂ generate same simple lottery.