Relative & Expected Frequency Flashcards

All 7 cards in this deck

What is relative frequency (experimental probability)?

$\dfrac{\text{number of times the outcome happened}}{\text{total number of trials}}$

What is the formula for expected frequency (an estimate of the number of successes)?

Expected frequency $=$ probability $\times$ number of trials.
e.g. $0.2 \times 60 = 12$

Whose results give the best estimate of a probability, and why?

The person with the greatest number of trials — a larger sample gives a better estimate.

True or false? An expected frequency tells you exactly how many times the outcome will occur.

False.
It is only an estimate of the number of times.

True or false? As the number of trials increases, the relative frequency tends to get closer to the theoretical probability.

True.
Larger unbiased samples tend towards the theoretical probability.

What are the steps to decide whether a dice is fair or biased from experimental results?

e.g. a dice is rolled 60 times and lands on six 25 times

1. Theoretical probability if fair: $\frac{1}{6}$
2. Expected frequency: $\frac{1}{6}\times 60 = 10$
3. Compare with the relative frequency/actual result: 25 is much greater than 10, so the dice is probably biased.

True or false? A spinner with red, blue, green and yellow sections that lands on red 7 times out of 20 spins must be biased.

False. A small difference from the expected result can happen by chance; bias is only suggested when the relative frequency is very different from the theoretical probability over many trials.