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November 2nd, 2017, 07:11 PM  #1 
Newbie Joined: Oct 2017 From: United States Posts: 7 Thanks: 1  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? Thanks! 
November 2nd, 2017, 07:53 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,039 Thanks: 1063 
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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