What is the formula for relative frequency?

\frac{number of times the outcome happens}{total number of trials}

What is the formula for expected frequency?

probability\timesnumber of trials

What happens to relative frequency as the number of trials increases?

It tends to get closer to the true probability.

Why is a result from 1000 trials more reliable than one from 20 trials?

More trials reduce the effect of chance, so the relative frequency is closer to the true probability.

What is theoretical probability?

The probability worked out from equally likely outcomes, without doing an experiment.

What does it suggest if experimental and theoretical probabilities are close?

There is no evidence that the object is biased.

How can you combine two sets of experimental results?

Add the successes and add the trials, then divide: \frac{total successes}{total trials}.

Is an expected frequency guaranteed to happen?

No. It is an estimate; the actual result is usually close but varies.

Experimental probability and expected frequencyIB MYP Maths Extended: Flashcards

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What is experimental probability?

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What is experimental probability?: A probability estimated from the results of trials.
What is the formula for relative frequency?: $\frac{\text{number of times the outcome happens}}{\text{total number of trials}}$
What is the formula for expected frequency?: $\text{probability}\times\text{number of trials}$
A spinner lands on blue 18 times in 60 spins. What is the relative frequency of blue?: $\frac{18}{60}=0.3$
How many 6s do you expect from a fair die rolled 300 times?: $\frac{1}{6}\times300=50$
What happens to relative frequency as the number of trials increases?: It tends to get closer to the true probability.
Why is a result from 1000 trials more reliable than one from 20 trials?: More trials reduce the effect of chance, so the relative frequency is closer to the true probability.
What is theoretical probability?: The probability worked out from equally likely outcomes, without doing an experiment.
What does it suggest if experimental and theoretical probabilities are close?: There is no evidence that the object is biased.
What does it suggest if the relative frequency stays far from the theoretical probability after many trials?: The object is probably biased.
How can you combine two sets of experimental results?: Add the successes and add the trials, then divide: $\frac{\text{total successes}}{\text{total trials}}$ .
Is an expected frequency guaranteed to happen?: No. It is an estimate; the actual result is usually close but varies.

Exam questions on Experimental probability and expected frequency

A spinner at a school in Kuala Lumpur has four equal sections, one of which is red. It is spun 200 times and lands on red 46 times.
Work out the theoretical probability of red and comment on whether the spinner appears to be fair.2 marks
A factory in Penang tests 400 light bulbs from one production line. Of these, 12 are faulty.
Suggest how the factory could get a more reliable estimate of the probability that a bulb is faulty, and explain why this works.2 marks
A student in Santiago flips a drawing pin 150 times and it lands point up 63 times. Another student flips the same pin 1000 times and it lands point up 412 times.
Work out the relative frequency of 'point up' for each student and state, with a reason, which is more reliable.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).