0
What is the probabililty of at least 2 people same birthday from a group of 13 people?
Wiki User
∙ 11y ago
19.4%
CALCULATION:
The probability of at least 2 people having the same birthday in a group of 13
people is equal to one minus the probability of non of the 13 people having the
same birthday.
Now, lets estimate the probability of non of the 13 people having the same birthday.
(We will not consider 'leap year' for simplicity, plus it's effect on result is minimum)
1. We select the 1st person. Good!.
2. We select the 2nd person. The probability that he doesn't share the same
birthday with the 1st person is: 364/365.
3. We select the 3rd person. The probability that he doesn't share the same
birthday with 1st and 2nd persons given that the 1st and 2nd don't share the same
birthday is: 363/365.
4. And so forth until we select the 13th person. The probability that he doesn't
share birthday with the previous 12 persons given that they also don't share
birthdays among them is: 353/365.
5. Then the probability that non of the 13 people share birthdays is:
P(non of 13 share bd) = (364/365)(363/365)(362/365)∙∙∙(354/365)(353/365)
P(non of 13 share bd) ≈ 0.805589724...
Finally, the probability that at least 2 people share a birthday in a group of 13
people is ≈ 1 - 0.80558... ≈ 0.194 ≈ 19.4%
The above expression can be generalized to give the probability of at least x =2
people sharing a birthday in a group of n people as:
P(x≥2,n) = 1 - (1/365)n [365!/(365-n)!]
Wiki User
∙ 11y ago
Add your answer:
Earn +20 pts
What is the probabililty of at least 2 people same birthday from a group of n people then how large ned n for the probability to be greater than 0.5?
It is 1 - 365Cn/365n. This is greater than 0.5 for n greater than or equal to 23.
How likely is it that in a group of 15 people who don't know each other at least 2 share a birthday?
10^%
How many people must be in the room in order to guaratnee that at least two people share a birthday?
367
What are the odds of having kids with the same birthday but a different year?
In probability theory, the birthday problem, or birthday paradox[1] pertains to the probability that in a set of randomly chosen people some pair of them will have the same birthday. In a group of 10 randomly chosen people, there is an 11.7% chance. In a group of at least 23 randomly chosen people, there is more than 50% probability that some pair of them will both have been born on the same day. For 57 or more people, the probability is more than 99%, and it reaches 100% when the number of people reaches 367 (there are a maximum of 366 possible birthdays). The mathematics behind this problem leads to a well-known cryptographic attack called the birthday attack. See Wikipedia for more: http://en.wikipedia.org/wiki/Birthday_paradox
How many people are needed in a room before two of them share the same birthday?
For the chance to be at least 50% that two people share the same birthday, there needs to be 22 people. For the chance to be exactly 100% that two people share the same birthday, there needs to be 366 people. If there was 365 people, there would be a very small chance that each person in the room would have different birthdays. With 366 people, there are not enough individual days for every person to have a different birthday, so there has to be at least one pair.
What is the probabililty of at least 2 people same birthday from a group of n people then how large ned n for the probability to be greater than 0.5?
It is 1 - 365Cn/365n. This is greater than 0.5 for n greater than or equal to 23.
What is the probabililty of at least 2 people same birthday from a group of 12 people?
The probability of at least 2 people in a group of npeople sharing a common birthday can be expressed more easily (mathematically) as 1 minus the probability that nobody in the group shares a birthday. Consider two people. The probability that they don't have a common birthday is 365/365 x 364/365. So the probability that they do share a birthday is 1-(365/365 x 364/365) = 1-365x364/3652 Now consider 3 people. The probability that at least 2 share a common birthday is 1-365x364x363/3653 And so on so that the probability that at least 2 people in a group of n people having the same birthday = 1-(365x363x363x...x365-n+1)/365n = 1-365!/[ (365-n)! x 365n ]In the case of 12 people this equates to 0.16702 (or 16.7%).
How likely is it that in a group of 15 people who don't know each other at least 2 share a birthday?
10^%
What is the probability that at least 2 people in a random group of 6 people have a birthday on the same day of the week?
1-365/[(365-6)*365^6] = 1 Is this O.K ?
What day is the least popular birthday?
when is your birthday? there's your answer...
Which group of people had the least amount of power in a manor?
On the manor, the people with the least power were the serfs.
How many people around the world share the same birthday as you?
A person shares their birthday with at least nine million different people around the world.
How many People share a birthday?
At least 100 all over the world.
Which group of americans is least represented by the government?
poor people
What group of people are least likely to commit suicide?
Greece
How many people must be in the room in order to guaratnee that at least two people share a birthday?
367
What group of people have the least lines and ridges on the tips of their fingers?
my wife
