Page 159 - Mathematics Coursebook

16.4 Estimating probabilities

16.4 Estimating probabilities

If you drop a thumb tack it can land point up or point down.
You cannot assume these two outcomes are equally likely.
You cannot use equally likely outcomes to #nd the probabilities.

However, you can do an experiment. point up point down total

!e table shows the outcomes when 80 thumb Outcome
tacks were dropped. Frequency 31 49 80
An estimate of the probability of ‘point up’ is 31 = 0.39 or 39%.
80

An estimate of the probability of ‘point down’ is 49 = 0.61 or 61%.
80

!ese are experimental probabilities. Probabilities found by using
equally likely outcomes are theoretical probabilities. The outcomes of tossing
What are the theoretical probabilities if the two outcomes are equally likely? a coin, either ‘heads’ or

!ey will both be 0.5. ‘tails’, are equally likely.
t Di$erent experiments on the same event could give di$erent experimental probabilities.

t !eoretical probabilities do not depend on an experiment and they do not change.
) Exercise 16.4
1 A survey of 40 cars on a particular length of road showed that 14 were speeding.
Find the experimental probability that the next car will be:
a speeding b not speeding.
2 There are 320 students in a school. 16 come to school by car. 96 walk to school.
Estimate the probability that a particular student:
a arrives by car b walks to school c does not walk to school d does not walk or come by car.

3 Mrs Patel goes to work by car each day. Sometimes she has to stop at a set of traffic lights.
In the past 25 working days she has had to stop 16 times.
a Find the experimental probability that she will have to stop at the lights tomorrow.
b Find the experimental probability that she will not have to stop at the lights next Wednesday.
4 Jasmine goes to school five days a week. In the last four weeks she has been late for school

on three days.
Estimate the probability that she will not be late for school tomorrow.
5 Carlos looks at the weather records for his town in November. Write your answer as a
Over the last five years (150 days) there has been rain on 36 days percentage or a decimal.

in November.
a Use this information to estimate the probability that it will rain on 1 November next year.
b Use the information to estimate the probability that it will not rain on 30 November next year.

6 Why might Razi’s method not be a good way to estimate the probability?

My team has won 18 of their last 20 matches, so the probability
that they will win their next match is 18 = 90%.
20

158 16 Probability