The events that cannot happen simultaneously or at the same time are called mutually exclusive events. \(\text{QS}, 1\text{D}, 1\text{C}, \text{QD}\), \(\text{KH}, 7\text{D}, 6\text{D}, \text{KH}\), \(\text{QS}, 7\text{D}, 6\text{D}, \text{KS}\), Let \(\text{B} =\) the event of getting all tails. 3.3: Independent and Mutually Exclusive Events Forty-five percent of the students are female and have long hair. \(\text{J}\) and \(\text{H}\) are mutually exclusive. The first card you pick out of the 52 cards is the \(\text{K}\) of hearts. Let event \(\text{B} =\) a face is even. On what basis are pardoning decisions made by presidents or governors when exercising their pardoning power? b. Of the fans rooting for the away team, 67% are wearing blue. If two events are mutually exclusive, they are not independent. Find the probability of the complement of event (\(\text{H OR G}\)). Let \(\text{F}\) be the event that a student is female. (There are three even-numbered cards: \(R2, B2\), and \(B4\). 7 Improving the copy in the close modal and post notices - 2023 edition, New blog post from our CEO Prashanth: Community is the future of AI, Probability of a disease with mutually exclusive causes, Proving additional formula for probability, Prove that if $A \subset B$ then $P(A) \leq P(B)$, Given $A, B$, and $C$ are mutually independent events, find $ P(A \cap B' \cap C')$. \(\text{H}\)s outcomes are \(HH\) and \(HT\). are licensed under a, Independent and Mutually Exclusive Events, Definitions of Statistics, Probability, and Key Terms, Data, Sampling, and Variation in Data and Sampling, Frequency, Frequency Tables, and Levels of Measurement, Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs, Histograms, Frequency Polygons, and Time Series Graphs, Probability Distribution Function (PDF) for a Discrete Random Variable, Mean or Expected Value and Standard Deviation, Discrete Distribution (Playing Card Experiment), Discrete Distribution (Lucky Dice Experiment), The Central Limit Theorem for Sample Means (Averages), The Central Limit Theorem for Sums (Optional), A Single Population Mean Using the Normal Distribution, A Single Population Mean Using the Student's t-Distribution, Outcomes and the Type I and Type II Errors, Distribution Needed for Hypothesis Testing, Rare Events, the Sample, and the Decision and Conclusion, Additional Information and Full Hypothesis Test Examples, Hypothesis Testing of a Single Mean and Single Proportion, Two Population Means with Unknown Standard Deviations, Two Population Means with Known Standard Deviations, Comparing Two Independent Population Proportions, Hypothesis Testing for Two Means and Two Proportions, Testing the Significance of the Correlation Coefficient (Optional), Regression (Distance from School) (Optional), Appendix B Practice Tests (14) and Final Exams, Mathematical Phrases, Symbols, and Formulas, Notes for the TI-83, 83+, 84, 84+ Calculators, https://www.texasgateway.org/book/tea-statistics, https://openstax.org/books/statistics/pages/1-introduction, https://openstax.org/books/statistics/pages/3-2-independent-and-mutually-exclusive-events, Creative Commons Attribution 4.0 International License, Suppose you know that the picked cards are, Suppose you pick four cards, but do not put any cards back into the deck. So, the probabilities of two independent events add up to 1 in this case: (1/2) + (1/2) = 1. then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format,