Answer:
The answer is: 27/216 = 0.125
Step-by-step explanation:
Since the dices are rolled and are fair. We can assume randomness of observation.
A is an event of even number from 1st die
B is an event of even number from 2nd die
C is an even of even number from 3rd die.
=> The number of possible outcome or sample space is 6^3 = 216.
=> Since each die has 3 even number each, the possibility of even number showing is 3^3 = 27.
When the dice is rolled, for even outcomes we have the following:
(2,2,2), (2,4,2), (2,6,2), (4,2,2), (4,4,2), (4,6,2), (6,2,2), (6,4,2), (6,6,2), (6,2,2),
(6,4,2), (6,6,2), (2,2,4), (2,4,4), (2,6,4), (4,2,4), (4,4,4), (4,6,4), (6,2,4), (6,4,4), (6,6,4), (2,2,6), (2,4,6), (2,6,6), (4,2,6), (4,4,6), (4,6,6), (6,2,6), (6,4,6), (6,6,6).
If we observe the outcomes, it is 27 outcomes for the even outcomes. And all possible outcomes is 6^3 = 216.
Then, the probability of even outcomes from each die from the roll is:
P(even) = (3^3)/(6^3) = (27)/(216) = 1/8 = 0.125
