# Independent Events Formula

If you roll a die twice, what are the odds that you will roll a number less than three followed by a number greater than two?

Let's see. There are are two ways you can roll a number less than three—either you roll a one or you roll a two. There are four ways you can roll a number greater than two—by either rolling a three, a four, a five, or a six.

From our work on ways of counting, we know that there are 2 * 4 = 8 ways that these two rolls can happen. Here they are: 1-3, 1-4, 1-5, 1-6, 2-3, 2-4, 2-5, 2-6.

What is the total number of possible outcomes for the two rolls? Since there are six numbers on a die, the total number is 6 * 6 = 36.

Using the probability formula, we can see that the probability of a number less than three followed by a number greater than two is 8/36 = 2/9.

There's another way to calculate these odds. The probability of rolling a number less than three and then rolling a number is greater than two is (2 * 4) / (6 * 6) = (2/6) * (4/6) = (1/3) * (2/3) = 2/9.

Notice that (2/6) * (4/6) is the probability for the first roll times the probability for the second roll.

In general, for independent events, you can find the probability of all the events happening together by multiplying together the probabilities of each event.