Mathematics - International - 0607 CIE

Relative And Expected Frequencies

Akopọ

Not every probability can be worked out by counting equally likely outcomes. What is the chance a drawing pin lands point up, or that a particular footballer scores a penalty? For these we have to experiment, and that is where relative frequency comes in: we run trials, record what happens, and use the results to estimate the probability.

In this lesson you will learn how relative frequency estimates a probability from real data, and why more trials give a better estimate. You will then turn the idea around: given a probability and a number of trials, you will predict how often an event should happen using expected frequency. Together these two ideas connect probability to the real world of experiments and surveys.

Awọn Afojusun

  1. Understand relative frequency as an estimate of probability.
  2. Calculate expected frequencies.

Akọ̀wé Ẹ̀kọ́

Theory only takes you so far. When outcomes are not equally likely, or when you simply do not know the true probability, you have to gather evidence. Manufacturers test products, scientists run experiments and pollsters survey voters precisely so they can estimate probabilities from real results. Relative and expected frequencies are the bridge between the tidy world of theory and the messy world of data.

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Ìdánwò Ẹ̀kọ́

Oriire fun ipari ẹkọ lori Relative And Expected Frequencies. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.

Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.

Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.

  1. A spinner is spun 200 times and lands on red 50 times. Estimate the probability of red. A. 0.1 B. 0.25 C. 0.4 D. 0.5 Answer: B
  2. The probability of an event is 0.2. In 50 trials, what is the expected frequency? A. 5 B. 10 C. 20 D. 25 Answer: B
  3. A fair die is rolled 120 times. How many times would you expect to roll a 4? A. 6 B. 12 C. 20 D. 24 Answer: C
  4. Which gives the most reliable estimate of a probability from an experiment? A. 5 trials B. 20 trials C. 100 trials D. 1000 trials Answer: D
  5. A bag of seeds has a germination probability of 0.9. Out of 300 seeds, how many are expected to germinate? A. 27 B. 90 C. 210 D. 270 Answer: D

O wa lori ohun elo Green Bridge

Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.

Awọn akọsilẹ ẹkọ ni kikun pẹlu awọn aworan apejuwe
Oluranlọwọ ẹkọ ti AI ṣe agbara rẹ
Kọ ẹkọ laisi intanẹẹti, nigbakugba, nibikibi
O wa lori Android, Windows, macOS, ati Linux

O wa lori ohun elo Green Bridge

Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.

Awọn akọsilẹ ẹkọ ni kikun pẹlu awọn aworan apejuwe
Oluranlọwọ ẹkọ ti AI ṣe agbara rẹ
Kọ ẹkọ laisi intanẹẹti, nigbakugba, nibikibi
O wa lori Android, Windows, macOS, ati Linux

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