A conditional probability question limits who can be selected before asking for a chance. The cue here is selected from students who brought a bottle: that group, not the whole festival, supplies the denominator. Restrict to the group being selected from before counting the target. Then use the row-column intersection for the numerator and divide in Desmos.
Hints
- Hint 1
In conditional probability, the group the student is selected from becomes the whole group of possible outcomes. Look at the bottle column: which total counts everyone who could be picked?
- Hint 2
The intersection is the cell where a row and column meet. Find where the environmental science row meets the bottle column. How many students satisfy both descriptions?
- Hint 3
A probability is the favorable count divided by the count of everyone who could be picked. Keep both counts in the bottle column, then type the fraction in Desmos.
Step-by-step
Restrict to the bottle column
Step 1Choose the group that could be picked
The student is selected from those who brought a reusable water bottle. This is the condition, the fact already known about the selected student. So only the bottle column counts, and its bottom total, , is the denominator. The students in the whole table include students who couldn't be picked.
- Step 2
Find the students who also chose the target track
Look for the intersection, where the environmental science row meets the bottle column. That cell contains students. They meet both requirements, so is the numerator. The row total of also includes students who didn't bring a bottle.
- Step 3
Write the probability
A conditional probability puts the count in both groups over the count in the selected-from group. The bar means “given that,” so put environmental science students with bottles over all students with bottles: .
- Step 4
Simplify the fraction
Type in Desmos. It shows about ; tap the fraction button to see . So the probability that the selected bottle-bringing student chose environmental science is . Choice D.