probability of having all are even or odd while throwing three dices
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Since 3 sides are even and 3 are odd, the chances of even = 3/6 = 1/2.
For three dice, probability of all even = (1/2)^3 = 1/2 * 1/2 * 1/2 = ?
Same is true for odd.
dice is already plural. No such word as dices.
well, the chance of any one die's being even or odd is 1/2
So, the chance of all three being even or all odd is (1/2)^3, since the events are independent.
To find the probability of getting three even or three odd numbers when throwing three dice, we first need to determine the sample space, which represents all possible outcomes.
Each dice has six possible outcomes: 1, 2, 3, 4, 5, or 6.
Since we are throwing three dice, the total number of possible outcomes is 6 * 6 * 6 = 216.
Now we need to determine the favorable outcomes, which are the outcomes where all three numbers are either even or odd.
Case 1: All three numbers are even.
There are three even numbers: 2, 4, and 6.
Therefore, the number of favorable outcomes for all three even numbers is 3 * 3 * 3 = 27.
Case 2: All three numbers are odd.
Similarly, there are three odd numbers: 1, 3, and 5.
Thus, the number of favorable outcomes for all three odd numbers is also 3 * 3 * 3 = 27.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = (27 + 27) / 216 = 54 / 216 = 1/4 = 0.25
Therefore, the probability of throwing three dice and getting all even or all odd numbers is 0.25 or 1/4.