Probability Of Combined Events
Bayani Gaba-gaba
Most interesting probability questions involve more than one thing happening: two dice rolled together, two coins tossed, a counter drawn then another. To handle these combined events we need organised ways of listing every possibility, and two simple rules for combining probabilities. Get organised and even busy-looking questions become straightforward.
In this lesson you will list outcomes with sample space tables, picture overlapping events, and follow the branches of a tree to combine probabilities. The two rules at the heart of it are short and memorable: multiply along the branches for AND, add the separate cases for OR. With these tools you can find the chance of almost any combined event.
Manufura
- Calculate the probability of combined events using, where appropriate: sample space diagrams Venn diagrams tree diagrams.
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- Two fair dice are rolled. What is the probability that the scores add up to 7? A. 1/12 B. 1/9 C. 1/6 D. 1/3 Answer: C
- Two fair coins are tossed. What is the probability of getting two heads? A. 1/8 B. 1/4 C. 1/2 D. 3/4 Answer: B
- A fair die is rolled. What is the probability of rolling a 2 or a 5? A. 1/6 B. 1/4 C. 1/3 D. 1/2 Answer: C
- Events A and B are independent with P(A) = 0.5 and P(B) = 0.4. What is P(A and B)? A. 0.1 B. 0.2 C. 0.5 D. 0.9 Answer: B
- Two fair dice are rolled. How many outcomes are in the sample space? A. 6 B. 12 C. 18 D. 36 Answer: D
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Sashen littafi
Tree and Venn Diagrams
Sometimes, when the probability problems are complex, it can be helpful to graph the situation. Tree diagrams and Venn diagrams are two tools that can be used to visualize and solve conditional probabilities. A tree diagram is a special type of graph used to determine the outcomes of an experiment.
"Introductory Statistics: Tree and Venn Diagrams" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/introductory-statistics/pages/3-5-tree-and-venn-diagrams. Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
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Sashen littafi
Two Basic Rules of Probability
When calculating probability, there are two rules to consider when determining if two events are independent or dependent and if they are mutually exclusive or not. If A and B are two events defined on a sample space , then: P ( A AND B ) = P ( B ) P ( A | B ). This rule may also be written as: P (
"Introductory Statistics: Two Basic Rules of Probability" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/introductory-statistics/pages/3-3-two-basic-rules-of-probability. Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
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