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15.4 Experimental and theoretical probabilities

Anders made a dice and threw it 300 times.
Score 1 2 3 4 5 6
He got these results.
b Anders is not correct. How could you convince him Frequency 45 58 48 48 46 55
that the dice may be fair?

The dice is biased because if I throw it 300 times, every
number should appear 50 times.

5 A group of five students want to find the
experimental probability of getting at least Student A B C D E
one 6 when throwing six dice. Each of them At least one 6 12 11 15 11 15
throws six dice 20 times to produce this data. Frequency
a Find the experimental probability of at No 6s 8 9 5 9 5
least one 6 from student A’s results.
b Find the experimental probability of at least one 6 by combining the results of:
i A and B ii A, B and C iii A, B, C and D iv A, B, C, D and E.
c What is the best estimate of the experimental probability?
The students repeated the experiment with another 20 throws each. At least one 6 70
The combined results this time were as shown.
d Calculate a new estimate for the experimental probability of throwing at No 6s 30
least one 6.
e In fact the theoretical probability for this outcome is 0.6651. How do the experimental
probabilities compare with this?

Summary

You should now know that: You should be able to:
★ If the probability of an outcome of an event ★ Use the probability of an outcome of an event
occurring is p, then the probability of it not occurring to find the probability it will not occur.
occurring is 1 − p. ★ Find probabilities based on equally likely
★ Probabilities can be based on equally likely outcomes in practical contexts.
outcomes in practical contexts. ★ Find and list systematically all possible outcomes
★ A good strategy for calculating probabilities is for single events and for two successive events.
listing systematically all possible equally likely ★ Compare estimated experimental probabilities
outcomes. with theoretical probabilities.
★ Experimental probabilities can vary from one ★ Use logical argument to interpret the mathematics
experiment to the next. in a context or to establish the truth of a statement.
★ Experimental probabilities are usually more
reliable if the experiment is repeated more often.
★ A logical argument can be used to establish the
truth of a statement.

156 15 Probability