A fair dice is rolled 3 times in a row. The outcomes are shown below.

Calculate the probability of all three events occurring.

Roll Outcome
1st 6
2nd factor of 12
3rd less than 6

25/216

Step-by-step explanation:

P( 6) = number of 6's / total number of outcomes

        =1/6

Then roll again

factor of 12: 1,2,3,4,6,12 =

1,2,3,4,6 are possible rolls = 5

P ( factor of 12)=number of numbers that are factor of 12 / total number of outcomes        = 5/6

Then roll again

P( number less than 6) = numbers less than 6 / total

                                      =5/6

P (6, factors of 12, number less than 6) = 1/6*5/6 *5/6

                                                                 =25/216

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!