# Measuring with a certain probability in Qiskit

I have the following quantum operation on two qubits: $$\mathcal{E}(\rho) = p \mathcal{T} \circ \mathcal{U}(\rho) + (1-p) \mathcal{U}(\rho) ​$$

where $$p$$ is some probability, $$\mathcal{U}$$ is some unitary operation on the two qubits and $$\mathcal{T}$$ measures whether both qubits are $$1$$.

I have the variable $$p$$ in Python, and I would like to use it to construct a circuit that implements the above. I tried to simply construct a circuit by making Python do the random choices (i.e. insert the measurement with probability $$p$$), but with this approach I need to recompile a new circuit for each shot, and I was wondering whether there is a simple way to make random choices directly within the QuantumCircuit.