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Hi! I would like to ask you some help with the question above. I think I didn't really understand the question. Could you help me please?

Thanks in advance.

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Consider a random sample with replacement of size $4$ from $4$ letters. What is the probability that at least three of the letters are the same?

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    The number of cases for the possible displacements are: $4^4$. Now, I consider the cases with exactly three letters being the same. I choose 2 from 4 to be the only letters that will appear. Then, I multiply by 2 to decide which letter will be 3 times-appeared and the one who appeared once and multiply by 4 to include the different positions of the single-appeared letter. That give us $$\frac{\binom{4}{2} . 2 . 4}{4^4}.$$Summing it with the probability of taking all equal letters that is 4 in $4^4$, I obtain the answer. Thanks I think I didn't understand before what the question meant. – 2017-01-19
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    Even though I still can not answer if this fact is or not random, i.e, if the younger sister is, in fact, clumsy. Could you help me with it? – 2017-01-20