A leader election algorithm is an elimination process that divides recursively into tow subgroups an initial group of n items, eliminates one subgroup and continues the procedure until a subgroup is of size 1. In this paper the biased case is analyzed. We are interested in the cost of the algorithm, i.e. the number of operations needed until the algorithm stops. Using a probabilistic approach, the asymptotic behavior of the algorithm is shown to be related to the behavior of a hitting time of two random sequences on [0,1].