You need to terminate client SSL traffic at the BIG-IP and also to persist client traffic to the same pool member based on a BIG IP supplied cookie. Which four are profiles that would normally be…

The TCP profile is essential for managing the underlying TCP connections, providing optimization and fundamental network layer control for all TCP-based traffic.

The HTTP profile is necessary to allow the BIG-IP to understand, parse, and manipulate HTTP traffic, which is required for inserting cookies for persistence and other HTTP-specific processing.

HTTPS is a protocol, not a configurable profile type on BIG-IP; its functionality is achieved by combining a ClientSSL profile with an HTTP profile.

The ClientSSL profile is explicitly required to perform SSL offloading, decrypting client-side encrypted traffic and terminating the client's secure connection at the BIG-IP.

A ServerSSL profile is only used when the BIG-IP needs to re-encrypt traffic before sending it to the backend servers, which is not a stated requirement for this scenario.

The Cookie persistence profile ensures that client requests are consistently directed to the same backend pool member by inserting and managing BIG-IP-generated HTTP cookies.