a number cube is rolled 2 times in a row. what is the probability of rolling a number greater than 2 both times?

To find the probability of rolling a number greater than 2 on a number cube rolled 2 times in a row, we need to determine the count of favorable outcomes and the total number of possible outcomes.

First, let's identify the possible outcomes for rolling a number cube. A standard number cube has six sides numbered 1 to 6. Hence, each roll has six possible outcomes: {1, 2, 3, 4, 5, 6}.

Next, let's determine the favorable outcomes, which are the outcomes where a number greater than 2 is rolled on both attempts. We can roll a number greater than 2 on any of the four faces: {3, 4, 5, 6}. Since we are rolling the number cube twice, the count of favorable outcomes would be 4*4 because each roll is independent. Therefore, the count of favorable outcomes is 16.

The total number of possible outcomes for two rolls of the number cube is 6*6 because each roll has 6 possibilities. Thus, there are 36 possible outcomes.

Finally, the probability of rolling a number greater than 2 on both attempts can be calculated by dividing the count of favorable outcomes by the total number of possible outcomes:

Probability = Count of Favorable Outcomes / Total Number of Possible Outcomes

Probability = 16 / 36

Simplifying the fraction, we get:

Probability = 4 / 9

Therefore, the probability of rolling a number greater than 2 on both attempts is 4/9 or approximately 0.44 (rounded to two decimal places).

Greater than 2 = 3, 4, 5 or 6.

One toss = 4/6 = 2/3

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.