from fault_web import FaultWeb

def update_fault_web(self, fault_web, fault_probabilities, dependencies):
    """
    Update the Fault Web visualization with the given fault probability information and dependencies between nodes.
    
    Args:
        fault_probabilities (dict): Dictionary mapping nodes to their fault probabilities.
        dependencies (dict): Dictionary representing the dependencies between nodes.
    
    Returns:
        object: Updated Fault Web object.
    """
    if not fault_web:
        fault_web = FaultWeb()
    
    # Add nodes and their fault probabilities to the fault web
    for node, probability in fault_probabilities.items():
        fault_web.add_node(node, probability)
    
    # Add edges representing dependencies with associated fault probabilities
    for node, adjacent_nodes in dependencies.items():
        for adjacent_node in adjacent_nodes:
            if node in fault_probabilities and adjacent_node in fault_probabilities:
                edge_probability = (fault_probabilities[node] + fault_probabilities[adjacent_node]) / 2
                fault_web.add_edge(node, adjacent_node, edge_probability)
    
    return fault_web.get_fault_web()