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November 2nd, 2017, 08:11 PM   #1
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Prob. Question

This is somewhat confusing to me.

[ Four people are selected at random. What is the probability that at least two of them were born on the same day of the week? ]


Any methods to solve this?

Do days of the week matter, perhaps?


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November 2nd, 2017, 08:53 PM   #2
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one has to assume that it's equally likely to be born on each day.

That's probably pretty close to being true, but it's an assumption nonetheless.

$\begin{align*}
&P[\text{2 or more born on same day of the week}] = \\ \\

&1 - P[\text{all born on different days of the week}] = \\ \\

&1 - \dfrac{7\cdot 6 \cdot 5 \cdot 4}{7^4} = \\ \\

&1 - \dfrac{120}{343} = \dfrac{223}{343} \approx 0.65

\end{align*}$
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