It is well-known that the fixed point theory plays a very important role in theory and applications. In 2017, Choi et al. [4] introduced the notion of bicomplex valued metric spaces (bi-CVMS) and established common fixed point results for weakly compatible mappings. On the other hand, in 1942, K. Menger [14] initiated the study of probabilistic metric spaces where he replaced the distance function $d(x,y)$ by distribution function $Fx,y(t)$, where the value of $Fx,y(t)$ is interpreted as the probability that the distance between $x$ and $y$ be less than $t$, $t>0$. In this paper, we have used bicomplex-valued metric on a set. We have taken $Fx,y(t)$ as the probability that norm of the distance between $x$ and $y$ be less than $t$, i.e., $||d(x,y)||0$ and initiated menger space with bicomplex valued metric. We also aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) or (E.A) property in this space.