Chapter 4 - Probability - 4-5 Multiplication Rule: Complements and Conditional Probability - Beyond the Basics - Page 175: 33

a)0.43. b)0.57.

a) The selections of birthdays are independent, hence we can us the multiplication rule: P(all bithdays are different)=$\frac{365}{365}\cdot\frac{364}{365}\cdot\frac{363}{365}\cdot...\frac{341}{365}=0.43.$ b)Here we can use the complement rule: P(at least 2 birthdays are the same=1-P(all bithdays are different)=1-0.43=0.57.