Conditional Probability
Gbogbo ọrọ náà
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.
Ebumnobi
- Calculate conditional probability using Venn diagrams, tree diagrams and tables.
Nkuzi Olu
Gee ntị na nkuzi a na ngwa
Maapụ uche
E seela isiokwu a ka ị hụ otu echiche si ejikọta.
Mepee maapụ uche na ngwa
Kaadị ncheta
Omume ncheta ngwa ngwa n'ihe a na-anwale n'isiokwu a.
Mee omume kaadị ndị a na ngwa
Akwụkwọ Ọmụmụ
Ndetu Nkuzi Zuru Ezu di na Ngwa Green Bridge
Nweta ngwa Green Bridge CBT na ekwenti gi ma o bu kompiuta maka ulo akwukwo IGCSE zuru oke: akwukwo ule ndi gara aga, usoro nyocha, eserese uche, kaadi omumu na nkuzi olu.
Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na Conditional Probability. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- 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
Rue ajuju ndi a n'ime ngwa ahu
Rue ajuju ndi a n'ime ngwa ahu
Akwụkwọ A Na-atụ Aro
Mụtakwuo ihe site na isi mmalite mepere emepe
-
Akụkụ akwụkwọ
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
-
Akụkụ akwụkwọ
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
Ndị otu ndị ọzọ bipụtara ha n'okpuru ikike mepere emepe, anyị na-ekele ha dị ka ha si chọọ. Njikọ na-emepe saịtị ha.
Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Conditional Probability? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
Budata Ngwa Ahụ Na Google Playstore
Ihe nile ichoro iji nwee ihe ịga nke ọma na JAMB, WAEC & NECO.
