In a two-way table, an intersection is the cell where a row and a column meet. For an and question, that cell counts the outcomes that match both descriptions. Divide by the full group that could be selected, unless the wording limits the selection to one row or column. The denominator comes from who can be picked, not where the matching cell sits.
Hints
- Hint 1
An intersection in a two-way table is the count where one row meets one column. The word with requires both descriptions to hold. Which cell counts townhouses that have solar panels?
- Hint 2
The sample space is every home that could be picked. The selection is from all 25 homes, not only the townhouses. Which table total counts that full group?
Step-by-step
Use the matching cell and the full total
Step 1Find the homes that match both descriptions
No Desmos needed. The table gives both counts for the probability fraction. Find the Townhouse row and the Solar panels installed column. Their intersection, the cell where they meet, is , so homes match both descriptions.
- Step 2
Choose the group that could be picked
The home is selected from all homes, not only the townhouses. The sample space, the full group that could be picked, has homes, so the denominator is . Using would answer a question about picking only from townhouses.
- Step 3
Write the probability
A probability is the matching count over the full count. Use the matching homes and all possible homes:
So the probability of selecting a townhouse with solar panels is . Choice C.