The basic formula in counting probability is the number of possible successful outcomes divided by the number of total outcomes. Here is an example of a fourth-grade-level counting probability question: If I roll a six-sided die, what is the probability that I roll a five? There is only one possible successful outcome: to roll the number "five." There are six sides on the die, so there are six total outcomes. Therefore, the probability is 1/6.
Geometric probability is used for calculation probability of regions. The basic formula for geometric probability is the size of the successful region divided by the size of the total region. Here is an example of a fourth-grade-level geometric probability question: If my father is between 38 years old and 45 years old, what is the probability that he is exactly 40 years old? In this question, the successful region is a size of one year, while the total size of the region is seven years. Therefore, the probability is 1/7.
Though solving probability algebraically is rare, it is still within the realm of use for advanced fourth-grade students. Let us use this question as our example: If I remove one marble from a bag that contains twice as many red marbles as blue marbles, and there are no marbles of other colors, what is the probability that the marble I removed is red? Because the marble will either be red or blue, the probability that it is blue is 1-X. The probability that it is red, then, is 2 times (1-X). If X = 2(1-X), then X = 2/3, which is our answer.
Probability always must be reduced to the least common denominator. This applies to all three of the aforementioned styles of probability. Because fourth-grade students are most likely to grasp counting probability, we'll revisit the example from Secion 1 and modify the question: If I roll a six-sided die, what is the probability that I roll either a five or a six? There are two possible successful outcomes, to roll either "five" or "six," out of six total outcomes. The probability, then, is 2/6. We then must reduce the probability to the least common denominator, which is 1/3.