Module 03 Determining Probability

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May 29, 2024

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Module 03 Determining Probability Determining Probability Compound Events In statistics, it is common to look at combining more than one event to find the probability. This section will look at finding the probability that either event A or event B occurs and the probability that both event A and event B occur. For the “OR” probability, addition and subtraction will be used to determine probability. Whereas, in the “AND” probability, multiplication will be used to determine probability.
Addition Rule We use the addition rule when trying to find the probability of an event A or an event B occurring. The word “or” in the addition rule is an “inclusive or” meaning that you can either have event A occur, event B occur, or both events occur. To find this probability, we take the number of ways event A can occur and add it to the number of ways event B can occur, but only so that each outcome is counted once. The formula is given below. The reason the probability of A and B is subtracted at the end is to take away any double-counting due to overlapping outcomes between events A and B (Triola & Iossi, 2018). Examples of Addition Rule Using the procedure of rolling a six-sided die once, what is the probability of the following compound events? Example 1 - What is the probability that you will roll an even number or number greater than 4? Recall that rolling a six-sided die produces six possible outcomes of the procedure: {1, 2, 3, 4, 5, 6}. The two events being looked at in this experiment are rolling an even number which has three outcomes: {2, 4, 6}, and rolling a number greater than four, which contains two outcomes: {5, 6}. Notice that there is one outcome, which is in both events: {6}. This means that the compound event of A and B would have 1 outcome. Using the formula above, the probability of rolling an even number or number greater than 4 would be
Example 2 - What is the probability that you will roll a five or a number less than 3? Recall that rolling a six-sided die produces six possible outcomes of the procedure: {1, 2, 3, 4, 5, 6}. The two events being looked at in this experiment are rolling a five, which only has one outcome: {5} and rolling a number less than three, which contains two outcomes: {1, 2}. Notice that they do NOT have any outcomes in common, so A and B would be empty. Using the formula above, the probability of rolling a five or a number less than 3 would be Notice in the example above that the two events of rolling a five and a number less than 3 resulted in the probability of 0. This indicates that the two events could never occur at the same time. When two events, A and B, cannot occur at the same time, these events are disjoint (or mutually exclusive ). When two events are disjoint, the addition rule simply becomes since the probability of A and B would be zero (Triola & Iossi, 2018).
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