Page 124 - Probability Demystified

CHAPTER 6 The Counting Rules 113

364 days left, so the probability that the second person was born on a
different day is 364 . The reasoning is the same for the next person. Now since
365
the probability is 0.992 that the three people have different birthdays, the
probability that any two have the same birthday is 1 0.992 ¼ 0.008 or 0.8%.
In general, in a room with k people, the probability that at least two people
will have the same birthday is 1 365 P k k .
365
In a room with 23 students, then, the probability that at least two students
23 ¼ 0:507 or 50.7%.
will have the same birthday is 1 365 P 23
365
It is interesting to note that two presidents, James K. Polk and Warren G.
Harding, were both born on November 2. Also, John Adams and Thomas
Jefferson both died on July 4. What is even more unusual is that they both
died on the same day of the same year, July 4, 1826. Another President,
James Monroe, also died on July 4, but the year was 1831.