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

To find the probability that a randomly chosen patient’s blood contains substance C, we sum the number of patients who have substance C. This includes:

• only C: 100
• A and C but not B: 100
• B and C but not A: 25
• A and B and C: 10 Thus, the total is: $100 + 100 + 25 + 10 = 235$. The probability is then calculated as follows: $P( ext{Substance C}) = \frac{235}{300} = \frac{47}{60}$.

Since Harry’s blood contains substance A, we focus on finding the probability of him having all three substances (A, B, and C) given he has A. The total cases where his blood holds A is:

• only A: 30
• A and C but not B: 100
• A and B but not C: 3
• A and B and C: 10 This gives a total of: $30 + 100 + 3 + 10 = 143$. The probability of him having all three substances is thus: $P(A\text{ and }B\text{ and }C | A) = \frac{10}{143}$.

The total number of patients surveyed is 300. To be a universal blood donor, a patient must have none of substances A, B, or C. From the given data, the section representing none of these substances (universal donor status) is:

• only C: 100
• A and C but not B: 100
• only A: 30
• B and C but not A: 25
• only B: 12
• A and B and C: 10
• A and B but not C: 3 So, the number of universal donors must be calculated as follows: Total patients with substances = 300 - (100 + 100 + 30 + 25 + 12 + 10 + 3) = 20. Therefore, the probability is: $P(\text{Universal donor}) = \frac{20}{300} = \frac{1}{15}.$