Probability
Visão Geral
A weather forecaster who says '70% chance of rain' is not guessing: that number comes from counting how often rain followed similar conditions in the past. Probability turns uncertainty into a precise number between 0 and 1, and once events start combining, whether one after another or at the same time, a small set of rules tells you exactly how to combine their probabilities correctly.
This topic builds the probability scale, sample spaces and relative frequency, then covers the addition rule for mutually exclusive events, the product rule for independent events, tree diagrams for combined and conditional events, very simple conditional probability, and expected frequency.
Objetivos
- Understand the language and basic concepts of probability including the probability scale, sample spaces, relative frequency, probabilities and complements
- Use the addition rule for two or more mutually exclusive events
- Use the product rule for two or more independent events
- Determine the probability of two or more independent events
- Use simple conditional probability for combined events using tree diagrams
- Find very simple conditional probability
- Understand and use the term expected frequency
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- P(rain) = 0.65. What is P(no rain)? A) 0.35 B) 0.65 C) 1.65 D) 0 Answer: A
- A fair die is rolled once. What is P(multiple of 2 or multiple of 3)? A) 1/6 B) 1/2 C) 2/3 D) 5/6 Answer: C
- Two fair coins are tossed. What is P(both land heads)? A) 1/2 B) 1/3 C) 1/4 D) 1/8 Answer: C
- A bag has 4 red and 6 blue counters. One is drawn and NOT replaced, then a second is drawn. What is P(second is red | first is red)? A) 4/10 B) 3/9 C) 4/9 D) 3/10 Answer: B
- A biased die has P(6) = 0.2. It is rolled 150 times. What is the expected number of sixes? A) 15 B) 20 C) 30 D) 75 Answer: C
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Secção do manual
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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Secção do manual
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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