For a statement like "Given that the listing has at least 2 bedrooms, the probability it has exactly 2 bedrooms," think: what goes in the numerator and what goes in the denominator of the probability fraction?

Write the fraction for

• numerator = number of suburban listings with exactly 2 bedrooms,
• denominator = number of suburban listings with at least 2 bedrooms,

and set this equal to $\dfrac{5}{9}$. Then solve for $p$.

In an expression line, type y = x/(x+20) to represent the probability of choosing a 2-bedroom suburban listing given that it has at least 2 bedrooms (where x stands for $p$).

In a new line, type y = 5/9 to graph the constant probability from the problem.

Zoom or adjust the window until you can see where the graph of y = x/(x+20) intersects the line y = 5/9. Click the intersection point and read off the x-value; that x-value is the value of $p$.

We are told: "If a randomly selected suburban listing has at least 2 bedrooms...".

That means we are only looking at suburban apartments with 2 bedrooms or 3 or more bedrooms.

From the table, in the Suburbs row:

• 2 bedrooms: $p$
• 3 or more bedrooms: $20$

So these are the only listings in our sample space for this probability question.

Within suburban listings that have at least 2 bedrooms, the total number of such listings is

• Number with exactly 2 bedrooms: $p$
• Number with 3 or more bedrooms: $20$

So the total number of suburban listings with at least 2 bedrooms is

We are given:

If a randomly selected suburban listing has at least 2 bedrooms, the probability that it has exactly 2 bedrooms is $\dfrac{5}{9}$.

In terms of counts, this probability is

From Step 2:

• with exactly 2 bedrooms is $p$.

• with at least 2 bedrooms is $p+20$.

So we must have

Now solve

Cross-multiply:

Distribute and simplify:

Divide both sides by 4:

So the value of $p$ is 25.