A probability model is a mathematical representation of a randomly occurring phenomenon. Probability is the study of the long-term behavior of random events in which the outcomes cannot be predicted. During the experiment, over the long term, patterns of results emerge. A probability 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 flipping a coin. When a coin is tossed and comes up heads three times, determining what outcome will occur on the fourth toss would be an assumption. Just because the coin lands on heads three times doesn't mean that the fourth coin toss will come up heads. In reality, the odds of one of the two events occurring (heads or tails) are 50%, 0.5 or ½. In the sample space of rolling two balanced dice we collect 36 different permutations. In the sample space we can identify distinct events within the 36 permutations. A distinct event is to result in two fair dice having a result where the sum of the two dice is a factor of 4. Results that have factors of 4 are (A, C), (B, B), (C, A ), (D, D), (F, B), (B, F), (E, C) and (C, E). There are 8 permutations that add up to 4. In the case of two fair dice being rolled there would be a probability of 8/36, which is simplified as 2/9, which is a 22% chance of receiving a result with the factor of 4 . A the second event receives a result in which both dice roll a result in which both dice land on a number less than 3. In the results of this distinct event we have (A, A1), (A, B), (B , A), and (B, B1). We have a total of four achievements in this distinct event. There is a 4/36, which is simplified as 1/9, or 11% chance of receiving a result where both independent dice are less than 3. Both probabilities are important for a step in studying treatments for many terrible diseases. If a drug is researched in its development phase, researchers calculate the maximum tolerated dose, considering that the dose has more toxic effects than health benefits.