A bag contains `2` red balls and `6` black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red?

Answer

1

Explanation

Equation is satisfied by `alpha,beta,alpha^(2)andbeta^(2)`. So, we have following possibilities:
(1) Let `alpha^(2)=alphaandbeta^(2)=beta`.
`implies(alpha,beta)-=(1,1)`
(ii) `alpha^(2)=betaandbeta^(2)=alpha`
`impliesalpha^(4)=alpha`
`impliesalpha(alpha^(3)-1)=0`
`impliesalpha=0,1,(-1pmsqrt3i)/(2)`
`implies(alpha,beta)-=((-1-sqrt3i)/(2),(-1+sqrt3i)/(2))`
(iii) `alpha^(2)betaandbeta^(2)=beta(oralpha^(2)=alphaandbeta^(2)=alpha)`
`impliesalpha^(2)=beta^(2)impliesalpha=pmbeta`
`implies(alpha,beta)=(-1,1),(1,1)` Thus, possible unordered pairs `(alpha,beta)` such that that `alphabetane0` is
`(1,1),(-1,1)or((-1-sqrt3i)/(2),(-1+sqrt3i)/(2))`.