Answer
$P(at~least~two~have~the~same~birthday)=0.1169$
Work Step by Step
$P(10~people~have~10~different~birthdays)\approx0.8831$
The event "at least two have the same birthday" is the complement of "10 people have 10 different birthdays".
Using the complement Rule (page 275):
$P(at~least~two~have~the~same~birthday)=1-P(10~people~have~10~different~birthdays)=1-0.8831=0.1169$