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Random beamforming has been considered as a practical scheme for MIMO BC system while achieving asymptotically optimal growth rate. However, this advantage is in terms of average sum rate performance, which is less meaningful when the quality of service is considered in system design. In this paper, we study the outage probability performance of random beamforming for both single receive antenna and multiple receive antenna with ZF receiver cases to consider the quality of service issues such as required data rate and outage probability itself. For single receive antenna case, the outage probability is lower bounded along with SNR due to its interference-limited nature. When multiple receive antennas are deployed at each user, the outage probability achieves the diversity of the number of users, but it has power penalty as much as the multiplexing gain. We also show exploiting multiple antennas at each user achieves larger multiplexing gain for given required data rate and outage probability. However, in low SNR regime, using single receive antenna reduces receiver complexity while achieving little performance degradation compared to multiple receive antenna case.