A person who got infected chicken pox is highly unlikely to get infected again in their lifetime. What kind of immunity is this?
Acquired immunity
Artificially acquired active immunity can be induced by a vaccine, a substance that contains antigen. A vaccine stimulates a primary response against the antigen without causing symptoms of the disease. The learning process starts when a person's immune system encounters foreign invaders and recognizes nonself substances (antigens). ... Acquired immunity is also called specific immunity because it tailors its attack to a specific antigen previously encountered.