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The following shows the results of a survey on the types of exercise taken by a group of 100 people - Edexcel - A-Level Maths Statistics - Question 6 - 2012 - Paper 1
Question 6
The following shows the results of a survey on the types of exercise taken by a group of 100 people. 65 run 48 swim 60 cycle 40 run and swim 30 swim and cycle 35 ru... show full transcript
Worked Solution & Example Answer:The following shows the results of a survey on the types of exercise taken by a group of 100 people - Edexcel - A-Level Maths Statistics - Question 6 - 2012 - Paper 1
Step 1
Draw a Venn Diagram to represent these data.
Answer
To draw a Venn Diagram:
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Label the circles as follows: R (Run), S (Swim), and C (Cycle).
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Place the number of individuals who do all three exercises (25) at the center where all circles intersect.
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From the numbers provided, calculate the values for those who do two exercises and only one exercise using the following formula:
- For Run and Swim: 40 - 25 = 15
- For Run and Cycle: 35 - 25 = 10
- For Swim and Cycle: 30 - 25 = 5
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Proceed to calculate those who only run, only swim, and only cycle as follows:
- Only Run: 65 - (15 + 10 + 25) = 15
- Only Swim: 48 - (15 + 5 + 25) = 3
- Only Cycle: 60 - (10 + 5 + 25) = 20
Lastly, attach the respective values in their segments on the Venn diagram.
Step 2
Find the probability that a randomly selected person from the survey takes none of these types of exercise.
Answer
First, determine the total number of individuals participating in the survey who take at least one type of exercise. This can be calculated as:
Total with at least one exercise = Total people - Those who take none = 100 - (15 + 3 + 20 + 15 + 5 + 10 + 25) = 7.
Thus, the probability that a randomly selected person takes none of these exercises:
Step 3
Step 4
Step 5
Find the probability that he swims but does not cycle.
Answer
Considering Jason runs, the results show that, under this condition, the number of individuals who swim but do not cycle remains as previously calculated at 8.
Since we are conditioning on him running, we revise total individuals as those who run:
Thus, from the 65 individuals who run, the probability that Jason swims but does not cycle is:
P(Swim \cap \neg Cycle | Run) = \frac{8}{65} = rac{8}{65}