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I'm studying for a midterm tomorrow and on the practice exam I've come across a question I can't seem to figure out.

A fair six-sided die is tossed four times, each time noting which numbered face lands up. What is the probability that at least two different numbered faces land up during the four tosses?

Thank You!

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up vote 3 down vote accepted

Hint: what is the probability that the same face pops up over the four rolls? The answer you seek is one minus this probability.

To attack this, consider what happens. You get a first roll and record what you get. The probability that the next 3 rolls give you that same face is...?

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So my chances of rolling any given face is 1/6. If I roll that 4 times in a row my probability is 1/(6^4) correct? Thus my answer should be 1 - (1/(6^4). Is this right? – jblittle Feb 23 '13 at 4:41
Not doesn't matter what you get on your first roll. The next 3 rolls have to be the same as that first one, however. – Ron Gordon Feb 23 '13 at 4:42
Oh I get it! It's 1- (1/(6^3)) and the first roll doesn't matter because it can't possibly give me the wrong face since it is, in fact, the first roll. Thanks a ton! – jblittle Feb 23 '13 at 4:48

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