# A 6 sided die is rolled four times. What is the probability of rolling a six on all four rolls?

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The roll has 6 sides, the probability of rolling a six when the die is rolled once is 1/6

When rolled 4 times, each time has a probability of 1/6.

Then the probability is:

1/6 * 1/6 *1/6 *1/6 = 1/ 6^4 = 1/1296

I believe we are talking about a 6 sided cubical dice marked with numbers 1 to 6 on the sides. In this dice the probability of getting any particular number on roll of a dice is 1/6>

Therefore the probability of getting a 6 in any one roll is 1/6.

Therefore the probability of getting a 6 in first roll is 1/6.

The probability of getting a six in first two rolls is:

= (Probability of getting a 6 in first roll)x(Probability of getting a 6 in second roll)

= (1/6)x(1/6) = (1/6)^2

Similarly the probability of getting a 6 in first 4 rolls = (1/6)^4

= 1/1296 = 0.0007716

The events of rolling 4 times are mutually indepedent.

Getting a 6 in one rolling 1/6.

The events being independent , getting 6 in all 4 thows is (1/6)^4 = 1/6^6.

Alternatively you get a number 6666 , among the 4 digit number whose each digits are 1 to 6 . So each place could be 1 to 6 and the total number of 4 digit numbers that is possible is 6^4. So 6666 is a one number out of 6^6 numbers. So the required probability is 1/6^4.

`1/6*1/6*1/6*1/6=1/6^4`

`1/1296`

``because there is a 1 out of 6 chance of getting a six on a roll the total chances of getting 4 sixes is one in 1296