dice problem- practice

[Guest]

Hello.I have this problem:
Two dices are rolled simultaneously. Calculate the probability that the maximum is greater than or equal to 3.

Solution :8/9

so I found that te total of outcomes is given by 6*6 since there are two dices.
Now what confuses me is the number of favorable outcomes that the exercise asks for, I tried with all of the combinations of dices greater and equal to 3 but it isn't the solution. Can you help me pls.

[HallsofIvy]

Yes, there are 6*6= 36 possible outcomes when you roll two dice. ("dices" is a verb, not a noun. As a noun "dice" itself is the plural of the singular "die".)

It is tedious but not difficult to list all 36. Count the number where the larger roll is greater than or equal to 3 and divide by 36. Equivalently, the possible outcomes of a single die are {1, 2, 3, 4, 5, 6}. Of those, 4, {3, 4, 5, 6}, are "greater than or equal to 3". How many pairs have at least one number "greater than or equal to 3"?