How to Calculate the Probability of 13 Out of 408 Guessing a Birthday Correctly?

In summary, the chance of 13 out of 408 people guessing someone's birthday correctly is approximately 1 in 5,370,675,393. This is calculated using the binomial distribution, assuming each guess is independent and ignoring leap years. The C function is used to calculate combinations and can be found using the formula C(n, k) = \frac{n!}{(k!)(n-k)!}.
  • #1
Arbu
6
0
If 408 people try to guess someone's birthday, how do you calculate the chance of 13 of them being right? http://www.greasypalm.co.uk/gpforum/forum14/363.html
 
Physics news on Phys.org
  • #2
Well, the chance of each individually being right is 1/365 (ignoring leap years and assuming people's guesses are independent of the person's actual birthday, which is probably not true), and if they are independent then it follows the binomial distribution, so the answer is
C(408, 13) * (1/365)^13 * (364/365)^395. Unless you're interested in the probability of at least 13 being right.
 
Last edited:
  • #3
Sorry, statistics represents a bit of a gap in my education. What is this C function, and how do I calculate it/look it up?

Let's go with exactly 13 of them being right.
 
  • #4
C(n, k) = [tex]\frac{n!}{(k!)(n-k)!}[/tex]
 
Last edited:
  • #5
Thanks. 1 in 5,370,675,393 I make it.
 

FAQ: How to Calculate the Probability of 13 Out of 408 Guessing a Birthday Correctly?

What is a simple statistical question?

A simple statistical question is a question that can be answered using basic statistical methods. It typically involves collecting and analyzing data to answer a specific question or make a prediction.

What are some examples of simple statistical questions?

Examples of simple statistical questions include: What is the average height of students in a class? How many people prefer chocolate ice cream over vanilla? Is there a correlation between exercise and weight loss?

What is the difference between descriptive and inferential statistics?

Descriptive statistics involve summarizing and describing data, while inferential statistics involve making predictions or drawing conclusions about a larger population based on a sample of data.

What is the importance of understanding simple statistical concepts?

Understanding simple statistical concepts is important for making informed decisions and drawing accurate conclusions based on data. It also helps to identify patterns and trends that may not be obvious at first glance.

What are some common misconceptions about simple statistics?

Some common misconceptions about simple statistics include thinking that correlation implies causation, assuming that a small sample size is representative of a larger population, and believing that statistical significance always means a result is important or meaningful.

Similar threads

Back
Top