Question 328009: A standard six-sided die is thrown four times. What is the probability that all
four rolls show a six? Found 2 solutions by stanbon, jessica43:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A standard six-sided die is thrown four times. What is the probability that all
four rolls show a six?
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(1/6)^4 = 0.000772..
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Cheers,
Stan H.
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You can put this solution on YOUR website! This type of probability is called joint probability with replacement. With replacement means that the object chosen on one stage is returned to the sample space before the next choice is made. Independent events are considered with replacement since they do not affect each other, interfere with each other, or cause each other. For example, tossing a head on the first toss does not affect the outcome of flipping the coin a second time.
The probability that independent events happen simultaneously is found by using the multiplication rule, or the product of the individual probabilities.
In this case, the probability of rolling a six on a six sided die is 1/6.
Now using this multiplication rule, to find the probability that all four rolls show a six, you multiply each individual probability:
(1/6)*(1/6)*(1/6)*(1/6)
= 1/1296
So the probability is 1/1296.
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