Related problems--what if you want the probability of someone's birthday being a particular day? The chances are much lower, and, in fact, no matter how many people in your group, you can't be sure someone will have a birthday on January 11th, for example. Our probabilities will be lower, but the strategy is the same:

• You should start with finding the probability that everyone has a birthday that is not on the day that you are interested in.
• You find the probability that the birthdays are different, by thinking about people 1 by 1:
  • What is the probability that the first person's birthday is not Jan 11?
  • What is the probability that the first person's birthday is not Jan 11?
  • What is the probability that the first person's birthday is not Jan 11? (notice that this is easier in some ways, because the question--and answer-- is the same every time)
  • etc.
• The complement of everyone having a that is not Jan 11 is (at least) one person's birthday being Jan 11.
• So, the P(someone's B-day is Jan 11) = 1-P(everyone's B-day is not Jan 11)

Some problems like this:

5. What computation would you do to figure out for a group of 8 people what the probability is that someone has a birthday of Jan 11? (just write out the mulitplication, don't crunch the numbers) (assume 366 equally likely days per year)

6. In a group of 8 people, what is the probability that someone has a birthday in January?

7. If everyone in a goup of 4 people rolls a 6 sided die, what is the probability that at least one person gets a 6?

8. If I roll a 6-sided die 6 times, what is the probability thta I get at least one 6?

9. If everyone in a group of 5 people rolls a 20 sided die, what is the probability that someone will get a 1?

And a few mixed up practice questions:

10. If I roll an 8-sided die 3 times, what is the probability that I get a different number every time?

11. If I roll a 12-sided die 4 times, what is the probability that I get a 3 at least once

12. If I roll a 6- sided die 5 times, what is the probability that I don't get a 2 on any of the rolls?

13. If I roll a 10 sided die 4 times, what is the probability that I get the same number twice?

Answers