Federated learning (FL) is a promising distributed learning framework where distributed clients collaboratively train a machine learning model coordinated by a server. To tackle the stragglers issue in asynchronous FL, we consider that each client keeps local updates and probabilistically transmits the local model to the server at arbitrary times. We first derive the (approximate) expression for the convergence rate based on the probabilistic client selection. Then, an optimization problem is formulated to trade off the convergence rate of asynchronous FL and mobile energy consumption by joint probabilistic client selection and bandwidth allocation. We develop an iterative algorithm to solve the non-convex problem globally optimally. Experiments demonstrate the superiority of the proposed approach compared with the traditional schemes.