Mathematics Specification A - 4MA1 PearsonEdexcel

Probability

Gbogbo ọrọ náà

Probability measures how likely an event is to happen, placing every outcome on a scale from impossible (0) to certain (1). This topic gives you the vocabulary, notation and calculation techniques that underpin risk assessment, game design, weather forecasting and medical testing.

You will learn to list outcomes systematically, calculate theoretical and experimental probabilities, combine events using the addition rule for mutually exclusive outcomes, and read probabilities from Venn diagrams. Higher-tier students extend these ideas to tree diagrams, independent events and conditional probability.

Ebumnobi

  1. Understand the language of probability
  2. Understand and use the probability scale
  3. Understand and use estimates or measures of probability from theoretical models
  4. Find probabilities from a Venn diagram
  5. Understand the concepts of a sample space and an event, and how the probability of an event happening can be determined from the sample space
  6. List all the outcomes for single events and for two successive events in a systematic way
  7. Estimate probabilities from previously collected data
  8. Calculate the probability of the complement of an event happening
  9. Use the addition rule of probability for mutually exclusive events
  10. Understand and use the term 'expected frequency'
  11. [Higher] Draw and use tree diagrams
  12. [Higher] Determine the probability that two or more independent events will occur
  13. [Higher] Use simple conditional probability when combining events
  14. [Higher] Apply probability to simple problems

Maapụ uche

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Kaadị ncheta

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Akwụkwọ Ọmụmụ

When a doctor says a vaccine is 95% effective, or a weather app shows a 30% chance of rain, they are not guessing. They are using probability: a branch of mathematics that turns uncertainty into a number you can reason with. In this topic you will build the tools to do the same, starting with everyday language and ending with powerful combination rules that handle multi-step problems.

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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.

  1. A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4? A) 1/6 B) 1/3 C) 1/2 D) 2/3 Answer: B
  2. Events A and B are mutually exclusive. P(A) = 0.3 and P(B) = 0.5. What is P(A or B)? A) 0.15 B) 0.2 C) 0.8 D) 1.0 Answer: C
  3. The probability of an event happening is 0.35. What is the probability of it not happening? A) 0.35 B) 0.45 C) 0.55 D) 0.65 Answer: D
  4. A biased spinner lands on red 45 times out of 150 spins. What is the estimated probability of landing on red? A) 45/150 B) 1/3 C) 3/10 D) Both A and C Answer: D
  5. A bag contains 5 red and 7 blue counters. One counter is drawn at random. What is the probability it is blue? A) 5/12 B) 7/12 C) 5/7 D) 7/5 Answer: B

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