Disjoint (mutually exclusive) Events
Disjoint events, also known as mutually exclusive events, refer to a concept in probability theory
Disjoint events, also known as mutually exclusive events, refer to a concept in probability theory. Two events are said to be disjoint if they cannot occur at the same time or in the same outcome. In other words, if one event happens, then the other event cannot occur simultaneously.
For example, let’s consider the roll of a regular six-sided die. We can define two events: Event A is rolling an odd number (1, 3, or 5), and Event B is rolling an even number (2, 4, or 6). These events are disjoint because no outcome can be both odd and even simultaneously.
Mathematically, we can represent disjoint events using set notation. Let A and B be two events. If A and B have no outcomes in common, we can write it as:
A ∩ B = Ø,
where the symbol “∩” represents the intersection of sets and “Ø” represents the empty set.
To further illustrate the concept, let’s consider another example. Imagine rolling a fair six-sided die. We can define the following events:
Event C: Rolling an even number greater than 2 (4 or 6)
Event D: Rolling an odd number less than 3 (1)
In this case, Events C and D are also disjoint because there are no numbers that satisfy both conditions of being an even number greater than 2 and an odd number less than 3.
To determine the probability of disjoint events, we can sum the probabilities of the individual events. For example, if the probability of rolling an odd number on a six-sided die is 1/2 and the probability of rolling an even number is also 1/2, the probability of rolling either an odd or even number would be:
P(A ∪ B) = P(A) + P(B) = 1/2 + 1/2 = 1.
It is important to note that the sum of probabilities of disjoint events equals 1 since one of the events must occur.
In conclusion, disjoint or mutually exclusive events are events that cannot happen at the same time or in the same outcome. They have no outcomes in common, and their probabilities can be summed to find the probability of either event occurring.
More Answers:
Understanding the Probability of Events A or B | Mutually Exclusive and Non-Mutually Exclusive ScenariosUnderstanding Conditional Probability | A Powerful Tool for Accurate Predictions and Decision-Making
Calculating Conditional Probability | A Step-by-Step Guide for Probability Theory.