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edit approved Dec 5, 2020 at 12:17
Alejandro Bergasa Alonso
edit approved Dec 5, 2020 at 12:17
Alejandro Bergasa Alonso
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I came across a variation of the birthday problem asking "in a room of 4$4$ people what is the probability that at least 3$3$ of them share the same birthday".

I was unsure of the answer and thought that it would be P(3$3$ share the same birthday) + P(4$4$ share the same birthday), which equals: 1*$\frac{1}{365^2}$ + 1*$\frac{1}{365^3}$$1\cdot\frac{1}{365^2} + 1\cdot\frac{1}{365^3}$, and this comes out to be around 0.0000075%$0.0000075$%.

However my friend said that he thinks to correctly calculate the answer, the probability of 4th$4$th person not having the same birthday should be included in the calculation somewhere.

What would be the correct probability of at least 3$3$ out of 4$4$ people sharing the same birthday, and how could you extend the problem to work out the probability of at least "x""$x$" out of "y""$y$" people having the same birthday?

I came across a variation of the birthday problem asking "in a room of 4 people what is the probability that at least 3 of them share the same birthday".

I was unsure of the answer and thought that it would be P(3 share the same birthday) + P(4 share the same birthday), which equals: 1*$\frac{1}{365^2}$ + 1*$\frac{1}{365^3}$, and this comes out to be around 0.0000075%.

However my friend said that he thinks to correctly calculate the answer, the probability of 4th person not having the same birthday should be included in the calculation somewhere.

What would be the correct probability of at least 3 out of 4 people sharing the same birthday, and how could you extend the problem to work out the probability of at least "x" out of "y" people having the same birthday?

I came across a variation of the birthday problem asking "in a room of $4$ people what is the probability that at least $3$ of them share the same birthday".

I was unsure of the answer and thought that it would be P($3$ share the same birthday) + P($4$ share the same birthday), which equals: $1\cdot\frac{1}{365^2} + 1\cdot\frac{1}{365^3}$, and this comes out to be around $0.0000075$%.

However my friend said that he thinks to correctly calculate the answer, the probability of $4$th person not having the same birthday should be included in the calculation somewhere.

What would be the correct probability of at least $3$ out of $4$ people sharing the same birthday, and how could you extend the problem to work out the probability of at least "$x$" out of "$y$" people having the same birthday?

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rb_048
rb_048
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Birthday probability question

I came across a variation of the birthday problem asking "in a room of 4 people what is the probability that at least 3 of them share the same birthday".

I was unsure of the answer and thought that it would be P(3 share the same birthday) + P(4 share the same birthday), which equals: 1*$\frac{1}{365^2}$ + 1*$\frac{1}{365^3}$, and this comes out to be around 0.0000075%.

However my friend said that he thinks to correctly calculate the answer, the probability of 4th person not having the same birthday should be included in the calculation somewhere.

What would be the correct probability of at least 3 out of 4 people sharing the same birthday, and how could you extend the problem to work out the probability of at least "x" out of "y" people having the same birthday?