How a stakeholder is chosen randomly in proof-of-stake? In PoS a group of stakeholders is selected randomly. Now, the question is if stakeholder_1 owns more coins than stakeholder_2, then he has more chance to be selected as a validator in comparison to stakeholder_2 ? or both of them have an equal chance in selecting process ?
There are various variables to consider.

Min Stake Age, Max Stake Age, Input Age, Input Size.
And then there is the version of PoS being use.

Min Stake Age determines an inputs eligibility, they must be older than this figure to stake.
Max Stake Age is the upper limit of input age used to determine Input Age.
Input Age is used a factor in PoSv1 to determine the input weight (note the code variable nCoinAge is the factor of Input Age * Input Size).
Input Size is the amount of coins in an input.

V1, which is PPC and descendants, uses Coin Age as a factor.
basically age * size,
whereas 
V2 and V3 only uses size.

Under V1, if stakeholder_2 has less but older coins then they might have more chance.
Under V2 and V3 Input Age is removed form the equation, so the more eligible coins you have the greater your chances.