Within the rhesus negative group, how many people have blood type B? What expression represents the total number of rhesus negative people? Write the probability of picking a B– person as a fraction using these numbers.

You know the probability of picking a B– person (from the negative group) equals $1/9$. Set your fraction from the previous hint equal to $1/9$ and simplify the denominator $7+2+1$.

After simplifying, you should get a fraction of the form $\dfrac{2}{10 + x}$. Set it equal to $1/9$ and solve the resulting proportion by cross-multiplying.

In one line, type y = 2/(7 + 2 + 1 + x) and in another line type y = 1/9. These represent the two sides of the probability equation as functions of $x$.

You can also replace 7 + 2 + 1 with 10, so the first line is y = 2/(10 + x); this is equivalent and easier to read.

Look for where the two graphs intersect. Tap or click on the intersection point; Desmos will display its coordinates. The x-coordinate of this intersection is the value of $x$ that makes the probabilities equal.

The problem says “one of these people who is rhesus negative (–) is chosen at random.”

That means we are only choosing from the people in the rhesus – row, not from the whole table.

So the total number of possible people is the sum of the negative counts:

• Type A–: 7
• Type B–: 2
• Type AB–: 1
• Type O–: $x$

Total rhesus negative people: $7 + 2 + 1 + x$.

We are told that, given the person is rhesus negative, the probability that the person has blood type B is $1/9$.

Within the rhesus negative group:

• The number of B– people is 2.
• The total number of negative people is $7 + 2 + 1 + x$.

So the probability of B given negative is

Now simplify the denominator $7 + 2 + 1$.

Compute the sum in the denominator:

So the equation becomes

Now solve this equation for $x$.

Solve

Cross-multiply and simplify:

So the value of $x$ is 8.