Practice Paper 2

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Medium

1 mark

A laboratory is testing the effectiveness of a new indicator for the presence of a particular mineral in water. This mineral occurs naturally in approximately 8% of water sources.

The laboratory collected samples of water from several sources in the country. The country has been divided into different areas based on their geology and the number of samples taken from each area is proportional to the size of the area.

State the sampling method being used.

How did you do?

4 marks

It is intended that if the mineral is present in the water sample the test result will be "positive" and if the mineral is not present in the sample the test result will be "negative".

There is a certain amount of unreliability in the results of the test. 4% of samples that have the mineral present test negative. 89% of the samples that do not have the mineral present test negative.

The tree diagram shows some of this information.

q1-practice-paper2-setc-ib-dp-ai-sl

Write down the value of

a

ii)

b

iii)

c

iv)

d

How did you do?

8 marks

Use the tree diagram to find the probability that a water sample selected at random

will not have the mineral present and will test negative,

ii)

will test positive,

iii)

will have the mineral given that it tested positive.

How did you do?

3 marks

The scientists from the laboratory collected additional information about each sample: if the sample was taken from an area where livestock was present ( $L$ ), if the sample was within 100 miles of the laboratory ( $D$ ) and if the sample was tested in the laboratory within 24 hours of being collected ( $T$ ).

39 samples were taken from an area with livestock;
33 samples were taken within 100 miles of the laboratory;
36 samples were tested in the laboratory within 24 hours of being collected;
5 samples were taken from an area with livestock, within 100 miles of the laboratory and tested within 24 hours;
2 samples were taken from an area with livestock and within 100 miles of the laboratory but were not tested within 24 hours;
11 samples were taken within 100 miles of the laboratory and tested within 24 hours but were not taken from an area with livestock;
12 samples were tested within 24 hours but were not from an area with livestock nor were they taken from an area within 100 miles of the laboratory;
3 samples were taken from an area more than 100 miles from the laboratory without livestock and they were not tested within 24 hours of being collected.

Draw a Venn diagram to represent this information making sure that the diagram is labelled with all relevant information.

How did you do?

2 marks

Find the total number of water samples that were tested by the laboratory.

How did you do?

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Number of baskets	0	1	2	3	4	5	6
Frequency	41	17	34	31	10	15	2

DP IB Maths: AI SL

Practice Paper Questions

Practice Paper 2