A conditional probability question restricts which listings can be selected before you form a fraction. In a two-way table, use every part of the condition to find the eligible group, then put the count you want over that group's total. If a count is unknown, write the fraction first and use a Desmos regression to find it. Including excluded listings changes the denominator.
Hints
- Hint 1
For a conditional probability, the denominator counts only listings that could still be selected after the condition is applied. Which row and which bedroom columns satisfy both suburban and at least 2 bedrooms?
- Hint 2
The numerator counts the eligible listings with exactly 2 bedrooms. The denominator counts those listings plus the eligible listings with more bedrooms. How can you write those two counts using and the table?
- Hint 3
A regression lets Desmos find an unknown count. Replace with and the equals sign with , then read the fitted value under PARAMETERS.
Step-by-step
Restrict the table, then solve
Step 1Find the eligible listings
The selection is restricted to suburban listings with at least 2 bedrooms. Keep the suburban two-bedroom cell, , and the suburban three-or-more-bedroom cell, . So the eligible total is . Only listings that meet the condition belong in the denominator. The one-bedroom listings and the city-center row are excluded.
- Step 2
Write the probability equation
Within that group, the favorable count for exactly 2 bedrooms is . Put it over the eligible total and set the fraction equal to the given probability: .
- Step 3
Find the unknown count in Desmos
Type . Use for the unknown and to tell Desmos to fit the equation; typing would create a slider instead. Under PARAMETERS, Desmos shows . So there are suburban listings with exactly two bedrooms. Grid in 25.