The 6-sided die is thrown twice; find the probability that a number greater than 3 is rolled at least once.

In order to determine the probability that a number greater than 3 at least once fell out, you must use the formula for the classical definition of probability:

P (A) = m / n,

Where P (A) is the probability of the event A of interest to us, that is, if the number is greater than 3 at least once, m is the number of outcomes favorable to the event, n is the number of all equally possible outcomes of the test.

Let’s define all possible outcomes of dice rolls:

1 – 1, 1 – 2, 1 – 3, 1 – 4, 1 – 5, 1 – 6;

2 – 1, 2 – 2, 2 – 3, 2 – 4, 2 – 5, 2 – 6;

3 – 1, 3 – 2, 3 – 3, 3 – 4, 3 – 5, 3 – 6;

4 – 1, 4 – 2, 4 – 3, 4 – 4, 4 – 5, 4 – 6;

5 – 1, 5 – 2, 5 – 3, 5 – 4, 5 – 5, 5 – 6;

6 – 1, 6 – 2, 6 – 3, 6 – 4, 6 – 5, 6 – 6.

The first number is the number of points dropped on the first throw, the second – on the second. Let us underline the outcomes favorable to event A.

So m = 27, n = 36.

P (A) = m / n = 27/36 = 0.75.