Conditional Probability
Muhtasari
Sometimes one event changes the chance of another. If you draw a counter from a bag and keep it, the next draw is from a smaller bag, so the probabilities shift. Conditional probability is the mathematics of these knock-on effects: the probability of one event given that another has already happened.
In this Extended topic you will work with conditional probability using tables, Venn diagrams and tree diagrams. The classic setting is drawing objects without replacement, where each draw alters what remains. Once you see how the branch probabilities change after the first event, problems that look hard become a tidy multiplication along a path.
Malengo
- Calculate conditional probability using Venn diagrams, tree diagrams and tables.
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Hongera kwa kukamilisha somo la Conditional Probability. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.
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- A bag has 5 red and 3 blue counters. Two are drawn without replacement. What is P(both red)? A. 25/64 B. 20/56 C. 5/8 D. 4/7 Answer: B
- After drawing one red from a bag of 5 red and 3 blue (kept out), what is the probability the next is red? A. 5/8 B. 5/7 C. 4/7 D. 4/8 Answer: C
- Of 18 French students, 12 also study Spanish. A French student is chosen. What is P(studies Spanish)? A. 1/3 B. 2/5 C. 2/3 D. 12/30 Answer: C
- Which rule gives the probability of A and B in general? A. P(A) + P(B) B. P(A) x P(B given A) C. P(A) - P(B) D. P(A) / P(B) Answer: B
- A bag has 4 white and 2 black balls. Two are drawn without replacement. What is P(both white)? A. 4/9 B. 2/5 C. 1/3 D. 12/30 Answer: B
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Vitabu Vinavyopendekezwa
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Sehemu ya kitabu
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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Sehemu ya kitabu
Contingency Tables
A contingency table provides a way of portraying data that can facilitate calculating probabilities. The table helps in determining conditional probabilities quite easily. The table displays sample values in relation to two different variables that may be dependent or contingent on one another. Late
"Introductory Statistics: Contingency Tables" 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/3-4-contingency-tables. Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
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