Probability Experiments
This lesson covers:
- What 'fair' and 'biased' mean
- How to calculate relative frequency
- How to calculate expected frequency
Fair or biased
When rolling a regular six-sided die, the probability of rolling any particular number (for example, a 3) should be 1/6.
However, this will only be true if you have a 'fair' die - meaning every number is equally likely.
Some dice may be 'biased', which means they are more likely to land on some numbers than others. For example, it is possible to get dice that land on 3 almost every time.
Relative frequency To find the probability of an event occurring experimentally, we can carry out the event multiple times and see how often each outcome occurs. This allows us to calculate the relative frequency using the formula below: relative frequency = total no. of all outcomes no. of times an outcome happened |
For example: A fair die is rolled 100 times and lands on three 20 times. Calculate the relative frequency for landing on three. |
relative frequency = 100 20 =0.20 |
A fair die is rolled 80 times and lands on four 12 times. Calculate the relative frequency for landing on four.
Give your answer as a decimal to 2.d.p.
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A fair coin is flipped 48 times, and lands on heads 20 times. Calculate the relative frequency for landing on heads.
Give your answer as a decimal to 2.d.p.
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Are relative frequency and probability the same? No. The relative frequency should be roughly the same as the probability, but due to random chance, it is often different. |
For example, if you roll a fair die three times, you might roll '4' every time, which means you would calculate the relative frequency of '4' as 100%. However, this was just random chance. With a fair die, and six possible numbers, the probability of getting a '4' was actually 1/6 or 16.7%. |
To get as close as possible to the true probability, you should do a large number of trials. For example, as you repeat the dice roll, the relative frequency should get closer and closer to 16.7%. |
Expected frequency The expected frequency is an estimate of how many times you would expect something to happen if you do an experiment a certain number of times. |
expected frequency = probability x number of trials |
Example: If we roll a die 50 times, how many times would we expect it to land on '3'? (remember that the probability for landing on a certain number is 1/6) |
expected frequency = probability of landing on ‘3’ x number of times the die was rolled |
expected frequency =61× 50 =8.33 So we would expect the die to land on '3' eight times. |
The probability of a coin landing of heads is 50% (0.5).
If you flip a coin 320 times, what is the expected frequency of landing on heads?
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If you roll a die 432 times, how many times would you expect to have rolled a 5?
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