Penina was born in Jerusalem on 22 August 1922 to Yitzhak and Esther Ben-David, who made aliya from Odessa in 1919 on the Ruslan, which symbolized the beginning of the Third Aliyah. Her father was the first agricultural teacher in the Land of Israel, in the Tachkemoni School. He was a founder of the Hagana together with Zeev Jabotinsky, but he had to leave the house to hide from the British.
In 1935, the family moved to Nahalat Yehuda, in order to realize the dream of founding a creative farm in the Land of Israel. At a very young age, influenced by the Revisionist atmosphere of her home, Penina joined Beitar. Like all of the youths in the village, she participated in Hagana activities, training with firearms and Morse code. In 1939, amid the riots, she manned the station maintaining communications with Rishon LeZion.
In early 1940, she joined Lehi. She took firearms courses, recruited young women to Lehi, and supervised a cell. In 1941, while training with firearms, she was severely injured in her abdomen by a pistol shot. This left her vulnerable to pursuit by the CID.
In 1942, she married Ezra Tzur. In 1979, the Ministry of Defense recognized her disability.
In 1943, her firstborn son was born; in 1947, a daughter was born.
Penina was interested in the plastic arts, displaying her works in ten individual exhibitions and twenty group exhibitions. She was also involved in many activities for the benefit of the public.