27.2 Experimental probability and relative frequency


Experimental probability Imagine again that you have been asked to roll a number fi ve on a standard six-sided die. There is only one number fi ve on a standard six-sided die, and there are six numbers possible.


We can calculate the theoretical probability as P (5) = 1


__ 6


In real life, if we were to throw a fair die 12 times we would be unlikely to get exactly two number fi ves, as would be expected in theory. You can try it for yourself.


The experimental probability that something will happen is based on how often the event occurs, after collecting a large amount of data or running a trial (an experiment). It is based specifi cally on direct observations.


Frequency is how often (the number of times) an event occurs in a number of trials.


The relative frequency is the number of times that the event occurs during experimental trials, divided by the total number of trials conducted.


Relative frequency can be calculated using the following formula.


Relative frequency = number of successful trials the total number of trials


Discuss and discover


We already know how to calculate the probability of a simple event. For example if you toss a coin, the probability of heads is 1 probability of a tail is 1


20 times, you would get exactly ten heads and ten tails?


(i) Work with a classmate (or on your own) and toss a coin 20 times. Record your results in a table. You may want to use tally marks to help you keep count.


__ 2 . However, does this mean if you fl ipped a coin


__ 2 and the


Outcome


Number of heads Number of tails


(ii) What percentage of heads and what percentage of tails did you get? Does this number agree with the predicted probability?


(iii) Combine the results from your whole class in a table like the one below. Name Number of heads Number of tails


Total


Student 1 Student 2 …


Last student Total = Total = Total =


(iv) Now calculate the total percentage of heads that the whole class got, and calculate the percentage of tails that the whole class got. Are these values the same (or very close to) the predicted probability for a coin toss?


(v) How did the number of trials relate to the relative frequency of heads or tails on the coin? Tally Total


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Linking Thinking 1


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