S-CP How Do You Get to School?

All of the upper-division students (juniors and seniors) at a high school were classified according to grade level and response to the question "How do you usually get to school?" The resulting data are summarized in the two-way table below.

	Car	Bus	Walk	Totals
Juniors	96	122	56	274
Seniors	184	58	30	272
Totals	280	180	86	546

If an upper-division student at this school is selected at random, what is the probability that this student usually takes a bus to school?
1. \(\frac{58}{272}\)
2. \(\frac{180}{546}\)
3. \(\frac{122}{274}\)
4. \(\frac{58}{122}\)
5. \(\frac{272}{546}\)

If a randomly selected upper-division student says he or she is a junior, what is the probability that heor she usually walks to school?
1. \(\frac{56}{546}\)
2. \(\frac{86}{546}\)
3. \(\frac{56}{274}\)
4. \(\frac{86}{274}\)
5. \(\frac{274}{546}\)

Commentary

This task is designed as an assessment item. It requires students to use information in a two-way table to calculate a probability and a conditional probability. Although the item is written in multiple choice format, the answer choices could be omitted to create a short-answer task.

Solutions

Solution: Solution

Answer is (ii). \(P(\text{Bus}) = \frac{180}{546} = 0.330\)
Answer is (iii). \(P(\text{Walks}|\text{Junior}) = \frac{56}{274} = 0.204\)

How Do You Get to School? by illustrativemathematics, used under CC-BY-NC-SA 3.0