In hybrid free space optical/radio frequency (FSO/RF) systems, switching between the optical and RF links depends on the optical and RF signal to noise ratio (SNR) threshold levels; therefore, the correct choice of these threshold levels is essential to make best use of the complementary nature of optical and RF links. Optimal selection of these threshold levels is the prime objective of this paper. A hybrid FSO/RF system using modified switching scheme with two optical and one RF threshold is considered. Here, we propose an algorithm to obtain the optimized thresholds, which yield minimum bit error rate (BER) for a given outage probability under a constraint on maximum transmitted power. The optimized thresholds are dependent on the average optical and RF SNR. Hybrid FSO/RF system use both optical as well as RF power. The average system SNR is computed by considering the actual optical and RF power consumption. Also the performance of the hybrid FSO/RF system is studied with respect to average system SNR using optimized optical and RF thresholds. This analysis reveals the existence of a critical operating point of average optical SNR, beyond which the system should be preferably operated to ensure minimum BER.