Probability problem - birthdays

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In summary, the conversation discusses the probability of at least two people in a class of 30 having the same birthday. The person asking for help is unsure of how to solve the problem and turns to Google for assistance.
  • #1
Char. Limit
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Homework Statement


44. What is the probability that at least two people in your class (assume a class of 30 students) have the same birthday?

Homework Equations



I'm not sure, to be honest.

The Attempt at a Solution



I was helping out my roommate with his probability homework, and this question came up. I'm not sure how to answer it. How is this done?
 
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  • #3
Borek said:
http://lmgtfy.com/?q=same+birthday+probability

:-p

Ahaha... I did not know there was a Wikipedia article on what seemed to me to be just an unusually difficult homework problem. Thanks!
 

FAQ: Probability problem - birthdays

1. What is the probability that two people share the same birthday in a group of 23 people?

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.

2. How is the probability of shared birthdays calculated?

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.

3. Is there a specific date with the highest probability of shared birthdays?

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.

4. How does the probability change with a larger group size?

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.

5. What is the significance of the birthday problem?

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.

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