Question

We roll a die until we see each face at least once and let X be...

We roll a die until we see each face at least once and let X be the number of rolls needed for that to happen.

What is the formula for the probability that X= 6?

Give the exact value of E(X) as a simplified fraction.

Math   Statistics-And-Probability   
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Answer #1

We roll a die until we see each face once.

X is the number of throws required for this to happen.

We have to find the probability that X=6.

Now, each of the 6 throws can have 6 outcomes, namely 1, 2, 3, 4, 5 and 6.

So, all possible cases is 6^6.

Now, we have to get each face once.

So, the faces can be achieved in 6 throws in 6 throws, in 6! number of ways.

So, the favourable number of cases is 6!.

As we know, probability of an event is the ratio of the number of favourable cases of that event, to the number of all possible cases.

So, the required probability is

So, the answer is

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