Birthday Problem

[kellykav]

I have been stuck on this question for quite some time and it's due tomorrow.

a) Fill in the chart for a group of
[FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman]n [/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT]people where [FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman]p[/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT]([FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman]n[/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT]) is the probability of at least two of [FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman]n [/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT]people sharing the same birthday. Show the formula for each n that helped you to fill in the chart!

[FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman]n [/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT]	[FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman]p [/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT]
10
20
30
50

b) How many people must be in a room before the probability that some share a birthday becomes at least 50 percent? Use different values of

[FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman]n [/FONT][/FONT][FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman][/FONT][/FONT]in the formula and approximate to the nearest n. Show all work!

[FONT=Times New Roman,Times New Roman][FONT=Times New Roman,Times New Roman]
c) [/FONT][/FONT]Look up the birthdays of all of the Presidents of the United States. Are there any shared birthdays? What is the probability that this would occur? Explain and show all work using the formula. (FYI Obama is the 44th president but there have been only 43 presidents since Grover Cleveland served from 1885-1889 and 1893-1897 and is counted twice)

 

[tkhunny]

I don't see much effort.

Think of a calendar. If you lie up everyone at your party, and make them go check off their birthdate from the calendar. What is the probability that the day will be open for each?

First? 365/365 (Ignoring Leap Year)
Second? 364/365 <== If this is a match, we are done.
Third? 363/365 <== If this is a match, we are done.
and so on.

Where does this lead us?