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16.3 Using relative frequency

5 Two types of rechargeable battery are tested to see how long they will last.

At least 5 but At least 10 but At least 15 but
Time (hours) Up to 5
less than 10 less than 15 less than 20
Battery A 6 12 16 12

Battery B 18 20 15 12

a For each type of battery, estimate the probability that it lasts:
i 15 hours or more ii less than 10 hours.
b Which battery lasts longer? Give a reason for your answer.

6 A shop sells three makes of computer. This table Make Solong HQ Tooloo
shows how many were faulty within one year.
a Estimate the probability that each make will Number sold 420 105 681
be faulty.
b The shop started to stock a new brand, called Faulty within one year 28 19 32
Dill computers. It sold 63, but 7 were faulty
within a year. How does this make compare to the others?

7 Lynn planted three packets of seeds. The table shows how many germinated.
Packet of seeds Type A Type B Type C A seed germinates when

Number of seeds 24 38 19 it starts to grow.
Number that germinated 17 21 16

Which type is the most likely to germinate? Give a reason for your answer.
8 In archery you score up to 10 points for each Score 10 9 8 Fewer than 8
arrow. In a competion you shoot 60 arrows.
The table shows the results for one competitor. First 20 arrows 8 5 5 2
a Find the probability of scoring 9 or 10, Last 40 arrows 27 4 5 4
using:
i the first 20 arrows ii all 60 arrows.
b Did the competitor become more accurate as the competition went
on? Give a reason for your answer.

Summary

You should now know that: You should be able to:

+ If outcomes are mutually exclusive then only one + Know that the sum of probabilities of all mutually
of them can happen. exclusive outcomes is 1 and use this when solving
+ If a list of mutually exclusive outcomes covers all probability problems.
possible cases, then the probabilities add up to + Record and find all outcomes for two successive
one. events in a sample space diagram.
+ You cannot always find probabilities by using + Understand relative frequency as an estimate of
equally likely outcomes. probability and use this to compare outcomes of
+ You can use relative frequency to estimate experiments in a range of contexts.
probability. + Check results by considering whether the answer
is reasonable in the context of the problem.

156 16 Probability