To detect TCP and UDP ping sweeps on a network, the appropriate filter would be one that checks for packets directed at port 7, which is commonly used for the 'echo' service. This service is associated with ping functionality for both TCP and UDP protocols. Therefore, the correct filter to use would be Tcp.dstport==7 and udp.dstport==7, which checks for incoming packets where the destination port is 7 for both TCP and UDP traffic. This allows Mark to identify ping sweep attempts, as these would typically send packets to this port to elicit a response from the network.