Coincidental Birthdays

a. One couple attracted media attention when their three children, born in different years, were all born on July 4. Ignoring leap years, find the probability that three randomly selected people were all born on July 4. Is the probability low enough so that such an event is not likely to occur somewhere in the United States over the course of several years?

b. Ignoring leap years, find the probability that three randomly selected people all have the same birthday.