44. What is the probability that at least two people in your class (assume a class of 30 students) have the same birthday?
Borek said:
The probability of two people sharing the same birthday in a group of 23 people is approximately 50%. This is known as the birthday paradox, where the probability of a shared birthday increases dramatically as the group size increases.
The probability of shared birthdays is calculated using the formula P(n) = 1 - (365!/((365-n)!*365^n)), where n is the number of people in the group. This formula takes into account the number of possible combinations of birthdays in a group.
No, there is no specific date with the highest probability of shared birthdays. However, February 29th (leap day) has a slightly lower probability due to its occurrence every 4 years.
The probability of shared birthdays increases as the group size increases. For example, with a group of 50 people, the probability of shared birthdays is approximately 97%. This is due to the increased number of possible combinations of birthdays in a larger group.
The birthday problem has practical applications in fields such as cryptography and probability theory. It also demonstrates the counterintuitive nature of probability and highlights the importance of understanding sample sizes and combinations in statistical analysis.