H1954
This might make it simpler:-
Susan worked all her life, paid her contribution but made no payments to a personal pension so she was NOT contacted out.
Jenny worked all her life ( same number of years as Susan ) and paid into an occupational pension scheme so she WAS contacted out.
Susan gets full SP but Jenny gets reduced SP plus her Occupational Pension.
So many people have retired and asked me why their SP is less that their friends, and it's mainly because of the Occupational pension - sorry but we can't have our cake and eat it!
Mary did not work until her youngest child was 16, as her husband earned enough for her to afford to stay at home. She did not contribute NI from leaving to have her first child until the third was 16, 30 years later, and then paid voluntary contributions, (which are much lower than compulsory ones) for a few years until she had enough.
She gets the same pension as Susan, who was never able to afford not to work, and whose NI contributions subsidised the health and education of Mary's children.
Now that is having your cake and eating it.