How Do You Get to School?

Task

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.

1. 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. $\frac{272}{546}$

2. 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. $\frac{274}{546}$

IM 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.

Solution

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