Question

human blood can be classified into four common blood types - a, b, ab, and o. it is also characterized by the presence (+) or absence (-) of the rhesus factor. the table above shows the distribution of blood type and rhesus factor for a group of people. if one of these people who is rhesus negative (-) is chosen at random, the probability that the person has blood type b is $\frac{1}{9}$. what is the value of x?

Explanation:

Step1: Calculate total number of rhesus negative people

The total number of rhesus negative people is $7 + 2+1 + x=10 + x$.

Step2: Set up probability equation

The number of rhesus - negative people with blood type B is 2. The probability of choosing a rhesus - negative person with blood type B is $\frac{2}{10 + x}$. We know this probability is $\frac{1}{9}$. So we set up the equation $\frac{2}{10 + x}=\frac{1}{9}$.

Step3: Cross - multiply and solve for x

Cross - multiplying gives us $1\times(10 + x)=2\times9$. So $10 + x = 18$. Subtracting 10 from both sides, we get $x=18 - 10=8$.

Answer:

8