In a two-way table, conditional probability is the chance of an event within a group the question has already chosen. The phrase selected from tells you to use that group’s row or column total as the denominator. Read the count where it crosses the requested category, then divide in Desmos. Using the grand total answers a different question.
Hints
- Hint 1
Being selected from a group is a condition: it limits who can be picked before you calculate the probability. Which column contains everyone who could be selected, and what is its total?
- Hint 2
A favorable outcome is one that matches what the question asks about. Find where the morning row meets the column you chose. How many volunteers are in that cell?
Step-by-step
Restrict the group, then divide
Step 1Choose the group that can be selected
Planting herbs is the condition, the fact that limits who can be picked. So use the herbs column, whose total is . The group you select from supplies the denominator. The table’s volunteers include people who cannot be selected.
- Step 2
Find the morning count within that group
Where the morning row meets the herbs column, the table shows . These are the favorable outcomes: the herb planters who also worked the morning shift.
- Step 3
Write the probability
A probability is favorable outcomes divided by all possible outcomes. Only herb planters are possible here, so . The bar means given that the volunteer planted herbs.
- Step 4
Read the simplified fraction in Desmos
Type in Desmos. It shows ; tap the fraction button to see . So the probability that a volunteer selected from herb planters worked the morning shift is . Choice C.