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Probability basics and relative frequency
Probability measures how likely something is, from 0 (impossible) to 1 (certain).
Theoretical probability
P(event) = number of ways it can happentotal number of outcomes
P(rolling a 4 on a fair dice) = 16
The probabilities of all outcomes add to 1, so P(not A) = 1 − P(A).
P(rolling a 4 on a fair dice) = 16
The probabilities of all outcomes add to 1, so P(not A) = 1 − P(A).
Relative frequency
From an experiment: relative frequency = number of times it happenednumber of trials
More trials give a more reliable estimate.
Expected number of times = probability × number of trials.
More trials give a more reliable estimate.
Expected number of times = probability × number of trials.
Fair or biased
If relative frequencies from many trials are very different from the theoretical probabilities, the dice or spinner may be biased.
A spinner lands on red with probability 0.35. It is spun 200 times. How many reds would you expect?
- Expected = 0.35 × 200
Answer: 70
P = favourable ÷ total. All probabilities add to 1. Relative frequency = times it happened ÷ trials. Expected number = probability × trials.
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