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A person’s blood group is determined by whether or not it contains any of 3 substances A, B and C - Edexcel - A-Level Maths Statistics - Question 5 - 2008 - Paper 2
Question 5
A person’s blood group is determined by whether or not it contains any of 3 substances A, B and C. A doctor surveyed 300 patients’ blood and produced the table belo... show full transcript
Worked Solution & Example Answer:A person’s blood group is determined by whether or not it contains any of 3 substances A, B and C - Edexcel - A-Level Maths Statistics - Question 5 - 2008 - Paper 2
Step 1
Draw a Venn diagram to represent this information.
Answer
The Venn diagram should consist of three intersecting circles labeled A, B, and C. Each section of the circles should represent the number of patients corresponding to the table provided:
- Only C: 100 patients
- A and C but not B: 100 patients
- Only A: 30 patients
- B and C but not A: 25 patients
- Only B: 12 patients
- A and B and C: 10 patients
- A and B but not C: 3 patients
- The outside region (universal blood donors) can be computed as the total patients minus the sum of all patients within the circles.
Step 2
Find the probability that a randomly chosen patient’s blood contains substance C.
Answer
To find this probability, we need to sum up all patients who have substance C:
- Only C: 100
- A and C but not B: 100
- B and C but not A: 25
- A and B and C: 10
Total patients with substance C = 100 + 100 + 25 + 10 = 235.
Therefore, the probability is given by:
Step 3
Find the probability that his blood contains all 3 substances.
Answer
Given that Harry's blood contains substance A, we will consider the patients who have A. This includes:
- Only A: 30 patients
- A and C but not B: 100 patients
- A and B and C: 10 patients
- A and B but not C: 3 patients
Total patients with substance A = 30 + 100 + 10 + 3 = 143.
Out of these, the number of patients with all 3 substances is 10. Thus, the probability is:
Step 4
Find the probability that a randomly chosen patient is a universal blood donor.
Answer
Universal blood donors are those who contain none of substances A, B, or C. We can calculate this by first determining the total number of patients with any of the substances:
Total patients with A, B, or C = 300 - (100 + 100 + 30 + 25 + 12 + 10 + 3) = 20.
Therefore, the probability is: