© Published under licence by IOP Publishing Ltd. We measured The switching probability distributions of The first and second switches in Bi2-xPbxSr2-yLauCuO6+δ (BiPb2201) intrinsic Josephson junctions. The effective temperature of The first switch is temperature independent below 0.6 K, which is slightly higher than The crossover temperature estimated from The thermal activation model. On The other hand, The effective temperature of The second switch is temperature independent below 2.0 K, which is one-order higher than The crossover temperature. Our study shows that The temperature independent state at high temperature is measured not only in Bi2Sr2CaCu2O8+δ but also in Bi2Sr2CuO6+δ.