Determine the number of people needed to ensure that the probability at least two of them have the same day of the year as their birthday is at least 70 percent, at least 80 percent, at 90 percent, 95 percent, at least 98 percent, and at least 99 percent.

Solution Preview

Let's say the number of people needed to meet the probability is N. We will also assume that a year has 365 days (no leap years!).
The easiest way to think about it is to find the probability that NO two people have the same birthday. Then the probability that AT LEAST two people have the same birthday will be 1- (probability that NO two people have the same birthday).

We fix 'N' and determine the probability that no two people, in a room of N people, have the same birthday. Say that the people are
P(1),P(2),...,P(N). Now person P(1) may have any of the 365 days of the year for his birthday without contradicting the condition that no two people in the room will have the same birthday i.e. the ...

Solution Summary

The probablities of people having ths same birthday are investigated using permutations.

... are 6*6*6=216 possible outcomes of their birthdays. So, the probability that none were born on Saturday is ... of them there are 6 possible days for the birthday. ...

... both of them have their birth dates on different days'. So the probability that we have found out is P (Ac ... that both the women will have the same birthday is 1 ...

... First we estimate probability of NO TWO persons have birthday on same day. Take one by one person. 1st person has birth day on one of the 365 days. ...

... a) Using Excel, find the birthday problem probabilities for all ... can be found by first finding the probability that all n of the birthdays are different ...

... 2. The probability that at least two people have the same birthday is 1-P(all of them have different birthdays). There are 365 days in a year, and there are. ...

... 18 and 19: Birthdays Four people are selected at random. Assume 365 days in a year. 18. What is the probability that all four share the same birthday? 19. ...

... Number of ways in which 10 students can select different birthdays. ...Probability that each student has a different birthday (that is, no two students have the ...

... with the same birthday (same day, not same year ... Given a birthday of July 29th, please provide a detailed ... the street performer has a 2/3 probability of winning ...