A probabilistic model is a mathematical representation of a random phenomenon that occurs. Probability is the study of the long-term behavior of random events whose outcomes cannot be predicted. Over the course of long-term experience, patterns of results emerge. A probabilistic model includes its sample space, the events that occur in the sample space, and the possibilities associated with each event. When two events are independent, there is no correlation between the occurrence of one event and the occurrence of another event. The first event does not influence the outcome of the second. This can be seen in the example of tossing a coin. When a coin is tossed and comes up heads three times, determining what outcome will occur on the fourth toss would be guesswork. Just because the coin came up heads three times does not mean the fourth toss will come up heads. In fact, the chance of either event (heads or tails) occurring is 50%, or 0.5 or ½. In the sample space of rolling two fair dice, we collect 36 different permutations. In sample space, we can identify distinct events within the 36 permutations. A distinct event is the result of two fair dice where the result is that the sum of the two dice is a factor of 4. Results that have factors of 4 are (A, C), (B, B), (C, HAS). ), (D, D), (F, B), (B, F), (E, C) and (C, E). There are 8 permutations added together which are worth 4. In the event that two fair dice are rolled, there would be a chance of 8/36, which is simplified to 2/9, or a 22% chance of obtaining a result with a factor of 4. A the second event receives the result of both dice and receives the result of both dice landing on a number less than 3. In the results of this separate event we have (A, A1), (A, B ), (B, A), and (B, B1). We have a total of four results in this separate event. There is a 4/36, which is simplified by 1/9, or an 11% chance of obtaining a result where the two independent dice are less than 3. Both probabilities are important at one stage of the study of treatments for many dreaded diseases. If a drug is being researched at the development stage, researchers calculate the maximum tolerated dose, even though the dose has more toxic effects than health benefits..