What's the probability of throwing 4 out of 4 times an '8' , with 8-sided dice?

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Someone throws $4$ $8$-sided dice and all of them land on $8$. What's the probability of this event?

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Assuming fair die the probability of ruling an $8$ in one roll is the number of ways you can roll on $8$ (Either you do or you don't so that is $1$ way) divided by the number of ways you can roll anything. (There are eight things you can roll, so there are $8$ ways you can roll a die.)

If you do an event a multiple number of times and the result of doing it once has no bearing on the probability of doing it again (as is the case with rolling a die--- whatever you roll the first time will have no bearing what will happen the second time) the the probability of event A and also event B will be the probability of event A multiplied by the probability of event B.

So the probability of doing a single event $k$ times in a row, will be the probability of doing it once multiplied by itself $k$ times.

And that should give you ALL the information you need to figure this out.