Answer
$0.4313$
Work Step by Step
Because the birthdays of the people are independent, we can use the multiplication rule: $P(no \ people \ have \ the \ same \ birthday)=\frac{365}{365} \cdot \frac{364}{365} \cdot \frac{363}{365} \cdot \frac{362}{365} \cdot...\frac{341}{365}\approx0.4313$