₦airaland Forum

What's the probability that at least two student will have the same birthday in a class of 23? Let's assume there are 365 days in a year.
A. Over 50% chance
B. Less than 4% chance
C. Approximately 6.3% chance
D. Close to 0%

What's your answer and the reason for your answer. No need to show workings, just your reasoning/intuition is all I need.

Many people will fail this question because it is counter intuitive. It defies simple logic.

Close to Zero.

The sample size is not properly defined.

What's the age range of the students?

LogoDWhiz:
Close to Zero.

The sample size is not properly defined.

What's the age range of the students?

Sample Size is the entire student population in the world. Age Range is not relevant as Birthday is a day and is not dependent on age.

If the students were up to 32, there would be a 100% probability.
If 16, 50% probability.
If 23, over 50% probability

harrend:
If the students were up to 32, there would be a 100% probability.
If 16, 50% probability.
If 23, over 50% probability

Ok, and what's the reasoning behind your answer?

Obinoscopy:
Sample Size is the entire student population in the world. Age Range is not relevant as Birthday is a day and is not dependent on age.

I will still choose Close to Zero.

LogoDWhiz:
I will still choose Close to Zero.

Ok, and what is the reasoning behind your answer? No calculations need to be showed.

Birthday paradox hmm

A is the answer

Obinoscopy:
Many people will fail this question because it is counter intuitive. It defies simple logic.

Obinoscopy:
Ok, and what is the reasoning behind your answer? No calculations need to be showed.

The sample size is too big to have such a coincidence.

LogoDWhiz:
The sample size is too big to have such a coincidence.

Makes sense. However you are wrong. The answer doesn't make sense logically but can be proven mathematically. The question is called the Birthday Paradox and the answer is A (over 50% chance).

Obinoscopy:
Makes sense. However you are wrong. The answer doesn't make sense logically but can be proven mathematically. The question is called the Birthday Paradox and the answer is A (over 50% chance).

How?

I'd like to learn

LogoDWhiz:
How?

I'd like to learn

The reasoning behind it is to realize that the question is not about just one birthday being duplicated but any birthday so there are actually ²³C₂ ways to get a birthday match. And ²³C₂ is a pretty large number relative to the total possible combinations.

You can see the exact calculation on ChatGPT. I can still explain further if you feel ChatGPT is not explanatory enough.

Obinoscopy:
Many people will fail this question because it is counter intuitive. It defies simple logic.

Saw this together with the Monty Hall Problem. So I can prove mathematically but hard to make it make sense.


Mathematically, if A is probability of every 23 having separate birthday and B is the probability of at least 2 having the same.


Then , 1-A = B

Probability of A will be something like this

365/365 x 364/365 ....343/365. The decrease in the numerator considers that available birthday possible for the rest student has reduced by 1 continuously.

This totals less than 0.5.

To find B which is the question, 1-A will give you a number slightly greater than 0.5.




It is hard to make sense of it but it as mathematically accurate

Obinoscopy:
The reasoning behind it is to realize that the question is not about just one birthday being duplicated but any birthday so there are actually ²³C₂ ways to get a birthday match. And ²³C₂ is a pretty large number relative to the total possible combinations.

You can see the exact calculation on ChatGPT. I can still explain further if you feel ChatGPT is not explanatory enough.

Thanks boss