Answer
a. Becuase the first person can have a birthday on any of the 365 days but the second person can only on 364 days.
b. 0.99
c. 0.01
d. 0.41
e. 23 people
Work Step by Step
b. following the same logic as part a the probability that no 3 people share a birthday is $\frac{365}{365}$ * $\frac{364}{365}$ * $\frac{363}{365}$ $\approx$ 0.99
c. probability that E wont happen is P(notE) which is equal to 1-p(E). Thus we can use the probabilty from part b for p(E) and solve for 1-0.99 which equals 0.1
d. same method as a and b $\frac{365}{365}$ * $\frac{364}{365}$ * $\frac{363}{365}$ * ...... $\frac{346}{365}$ * $\frac{345}{365}$ $\approx$ 0.59 but since we need to fine 1-p(e) we solve 1-0.59=0.41
e. 1- ($\frac{365}{365}$ * $\frac{364}{365}$ * $\frac{363}{365}$ * ...... $\frac{343}{365}$ * $\frac{342}{365}$) $\approx$ 0.507
