Respuesta :
To find the probability that the 3 numbers on 3 dice rolled are different, we first calculate the total number of possible outcomes when rolling 3 dice. Each die has 6 sides, so the total number of outcomes for 3 dice is \(6 \times 6 \times 6 = 216\).
Next, we determine the number of ways we can have 3 different numbers on the dice. For the first die, we have 6 choices. For the second die, we have 5 choices (since it must be different from the first die). Finally, for the third die, we have 4 choices (as it must be different from the first two dice). Therefore, the number of ways to get 3 different numbers is \(6 \times 5 \times 4 = 120\).
Finally, we calculate the probability by dividing the number of successful outcomes (3 different numbers) by the total number of outcomes.
Probability = Number of successful outcomes / Total number of outcomes
Probability = 120 / 216
Probability = 5 / 9
Therefore, the probability that the 3 numbers on 3 dice rolled are different is 5/9 or approximately 0.5556.
