Leap days are the extra days (February 29) that are added to the Gregorian calendar in leap years.
Since each 400 years of the Gregorian calendar has

days, of which 97 are leap days, the probability P of being a leap day baby is

The following table summarizes the years in which the leap day falls on given weekdays for the years 1900-2100.
<DIV ALIGN="CENTER"> <TABLE CELLPADDING=3 BORDER="1"> <TR><TD ALIGN="LEFT">weekday</TD> <TD ALIGN="LEFT">leap years having that weekday at the leap day</TD> </TR> <TR><TD ALIGN="LEFT">Sunday</TD> <TD ALIGN="LEFT">1920, 1948, 1976, 2004, 2032, 2060, 2088</TD> </TR> <TR><TD ALIGN="LEFT">Monday</TD> <TD ALIGN="LEFT">1904, 1932, 1960, 1988, 2016, 2044, 2072</TD> </TR> <TR><TD ALIGN="LEFT">Tuesday</TD> <TD ALIGN="LEFT">1916, 1944, 1972, 2000, 2028, 2056, 2084</TD> </TR> <TR><TD ALIGN="LEFT">Wednesday</TD> <TD ALIGN="LEFT">1928, 1956, 1984, 2012, 2040, 2068, 2096</TD> </TR> <TR><TD ALIGN="LEFT">Thursday</TD> <TD ALIGN="LEFT">1912, 1940, 1968, 1996, 2024, 2052, 2080</TD> </TR> <TR><TD ALIGN="LEFT">Friday</TD> <TD ALIGN="LEFT">1924, 1952, 1980, 2008, 2036, 2064, 2092</TD> </TR> <TR><TD ALIGN="LEFT">Saturday</TD> <TD ALIGN="LEFT">1908, 1936, 1964, 1992, 2020, 2048, 2076</TD> </TR> </TABLE>
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If birthdays are distributed randomly throughout the calendar, then there would be approximately four million leap day babies in the world (assuming a world population of six billion). However, as the figure above and chart below show, some refinement of this estimate is needed since there is a decided peak in September for births in the United States between 1978-1987 (Peterson 1998).
<DIV ALIGN="CENTER"> <TABLE CELLPADDING=3 BORDER="1"> <TR><TD ALIGN="LEFT">month</TD> <TD ALIGN="LEFT">average daily birth frequency</TD> </TR> <TR><TD ALIGN="LEFT">January</TD> <TD ALIGN="LEFT">0.0026123</TD> </TR> <TR><TD ALIGN="LEFT">February</TD> <TD ALIGN="LEFT">0.0026785</TD> </TR> <TR><TD ALIGN="LEFT">March</TD> <TD ALIGN="LEFT">0.0026838</TD> </TR> <TR><TD ALIGN="LEFT">April</TD> <TD ALIGN="LEFT">0.0026426</TD> </TR> <TR><TD ALIGN="LEFT">May</TD> <TD ALIGN="LEFT">0.0026702</TD> </TR> <TR><TD ALIGN="LEFT">June</TD> <TD ALIGN="LEFT">0.0027424</TD> </TR> <TR><TD ALIGN="LEFT">July</TD> <TD ALIGN="LEFT">0.0028655</TD> </TR> <TR><TD ALIGN="LEFT">August</TD> <TD ALIGN="LEFT">0.0028954</TD> </TR> <TR><TD ALIGN="LEFT">September</TD> <TD ALIGN="LEFT">0.0029407</TD> </TR> <TR><TD ALIGN="LEFT">October</TD> <TD ALIGN="LEFT">0.0027705</TD> </TR> <TR><TD ALIGN="LEFT">November</TD> <TD ALIGN="LEFT">0.0026842</TD> </TR> <TR><TD ALIGN="LEFT">December</TD> <TD ALIGN="LEFT">0.0026864</TD> </TR> </TABLE> </DIV>
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The premise of Gilbert and Sullivan's musical The Pirates of Penzance is based on the birth of the main character on a leap day. In more modern times, there is website devoted to leap day babies.