Summer of '69.
Mr. John Doe was born on January 1st, 19xx.
It is known that January 1st, 1900 was a Monday and that Mr. John Doe died on in the summer of 1969.
If the probability that Mr. Doe was not born on a Thursday or a Saturday is given as , what is ?
The answer is 74.2857.
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1 solution
It is clear that Mr. Doe's birthday was January 1st and he was born in an year between 1900-1969. (i.e.,70 dates)
The number of days in a normal year is 3 6 5 = 1 m o d 7 and 3 6 6 = 2 m o d 7 .
The day on which 1st January falls on a particular year can be deduced as
J a n 1 ( x ) = { ( J a n 1 ( x − 1 ) + 1 ) m o d 7 , ( J a n 1 ( x − 1 ) + 2 ) m o d 7 , If x-1 is not a leap year If x-1 is a leap year
Using this formula and remembering that 1900 was not a leap year, it can be seen that January 1st was a Thursday in nine years (1909, 1915, 1920, 1926, 1937, 1943, 1948, 1954, 1965) and a Saturday for nine years (1905, 1911, 1916, 1922, 1933, 1939, 1944, 1950, 1961, 1967).
Thus, the probability of the year not starting on a Thursday or a Saturday is 7 0 7 0 − 1 8 = 0 . 7 4 2 8 6 = 7 4 . 2 8 6 %