This paper is concerned with the stochastic stabilization problem of observer-based output feedback control for sampled-data system. Different from most previous studies, we assume stochastic sampling and packet dropout may occur simultaneously. The packet dropouts lost in both the sensor-controller (S/C) and controller-actuator (C/A) channels are modelled by two mutually independent stochastic variables satisfying a two-state Markov Chain, and the system state is sampled with a stochastic sampling interval following a certain probability density. An observer-based sampled-data control scheme is proposed to estimate the states and system input simultaneously. A sufficient condition is derived for sampled-data system with simultaneous stochastic sampling and packet dropout via the Kronecker product operation and the Vandermonde matrix. Moreover, the corresponding stabilization controller is then designed based on a cone complementarity linearization algorithm.