Probability
Gbogbo ọrọ náà
An ordinary six sided dice is rolled 300 times and lands on five 120 times. Do you think the dice is fair? That is a real two mark question from a specimen Core paper, and answering it needs three separate ideas: what probability a fair dice gives, how many fives that predicts in 300 rolls, and how far an actual result can drift from a prediction before you should be suspicious. Fifty is expected, 120 was observed, and the gap is far too large to be luck.
You will use the vocabulary of probability and the probability scale, find probabilities from theoretical models and from relative frequency, work with expected frequency, compare experimental data with theoretical probabilities, understand why repeating an experiment gives different outcomes and why a larger sample gives better estimates, build sample spaces for one event and for two successive events, handle mutually exclusive and exhaustive outcomes, use Venn diagrams to work out probabilities, and calculate the probability of independent combined events including with tree diagrams. On the Extension Tier you add the addition rule for mutually exclusive events, the multiplication rule for independent events, and conditional probability.
Ebumnobi
- [Core] understand and use the vocabulary of probability and the probability scale
- [Core] understand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative frequency
- [Core] understand and use expected frequency
- [Core] compare experimental data and theoretical probabilities
- [Core] understand that if an experiment is repeated, this may - and usually will - result in different outcomes
- [Core] understand that increasing sample size generally leads to better estimates of probability and population characteristics
- [Core] understand and use sample spaces for situations where outcomes are single events and for situations where outcomes are two successive events
- [Core] identify different mutually exclusive and exhaustive outcomes and know that the sum of the probabilities of all these outcomes is 1
- [Extension] know and use that for mutually exclusive events A and B P(A ∪ B) = P(A) + P(B)
- [Core] understand and use Venn diagrams to work out probabilities
- [Core] calculate the probability of independent combined events, including using tree diagrams and other representations
- [Extension] know and use that for independent events A and B P(A ∩ B) = P(A) × P(B)
- [Extension] calculate conditional probabilities including using tree diagrams and other representations
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Akwụkwọ Ọmụmụ
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Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na 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 spinner has four equal sectors numbered 7, 1, 5 and 3. Which word describes the chance of landing on an odd number? A. impossible B. unlikely C. likely D. certain Answer: D
- An ordinary six sided dice is rolled 300 times. How many fives would you expect if the dice is fair? A. 5 B. 30 C. 50 D. 120 Answer: C
- A bag has 9 counters, 4 of them blue. Two are taken without replacement. What is the probability that neither is blue? A. 25/81 B. 20/72 C. 20/81 D. 5/9 Answer: B
- For which pair of events is P(A and B) = P(A) x P(B) always correct? A. Mutually exclusive events B. Exhaustive events C. Independent events D. All pairs of events Answer: C
- In a class of 30, 18 study French, 14 study Spanish and 6 study both. What is the probability that a student chosen at random studies neither? A. 2/15 B. 1/5 C. 4/15 D. 8/15 Answer: A
Rue ajuju ndi a n'ime ngwa ahu
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Akwụkwọ A Na-atụ Aro
Mụtakwuo ihe site na isi mmalite mepere emepe
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Terminology
Probability is a measure that is associated with how certain we are of outcomes of a particular experiment or activity. An experiment is a planned operation carried out under controlled conditions. If the result is not predetermined, then the experiment is said to be a chance experiment. Flipping on
"Introductory Statistics: Terminology" 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/3-1-terminology. Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
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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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Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Probability? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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