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What is the probability that both friends were born on the same day of the week?
What is the probability that 2 people chosen at random were born on the same day of the week. Answer: 1/7. Just take a random person.
What is the answer to the birthday problem?
Graphing the Birthday Problem Probabilities By assessing the probabilities, the answer to the Birthday Problem is that you need a group of 23 people to have a 50.73\% chance of people sharing a birthday! Most people don’t expect the group to be that small.
However, it is usual in the English-speaking world to call people who share the same birthday as “birthday twins.” Less frequently “Irish twins,” especially in the sense of same day and month but one year apart. Also found is “birthday buddy” (via Urban Dictionary).
What is the probability that two people have the same birthday?
The first person could have any birthday (p = 365÷365 = 1), and the second person could then have any of the other 364 birthdays (p = 364÷365). Multiply those two and you have about 0.9973 as the probability that any two people have different birthdays, or 1−0.9973 = 0.0027 as the probability that they have the same birthday.
How many possible combinations of birthdays are there in a group?
If one assumes for simplicity that a year contains 365 days and that each day is equally likely to be the birthday of a randomly selected person, then in a group of n people there are 365 n possible combinations of birthdays. The simplest solution is to determine the probability of no matching birthdays and then subtract this probability from 1.
What is the probability of sharing a birthday with 57 people?
: The probability of sharing a birthday = 1 − 0.294… = 0.706… Or a 70.6\% chance, which is likely! So the probability for 30 people is about 70\%. And the probability for 23 people is about 50\%. And the probability for 57 people is 99\% (almost certain!) We can also simulate this using random numbers.
In a bar with even a small crowd, if you can get someone to take your bet that two people share a birthday, you’ll win more often than you lose. In a randomly selected group of 50 people or more, it is nearly certain that two or more will share a birthday (p ≥ 97\%).