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# 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.

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?

- $\frac{58}{272}$
- $\frac{180}{546}$
- $\frac{122}{274}$
- $\frac{58}{122}$
- $\frac{272}{546}$

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?

- $\frac{56}{546}$
- $\frac{86}{546}$
- $\frac{56}{274}$
- $\frac{86}{274}$
- $\frac{274}{546}$

## 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

- 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?

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?

- $\frac{58}{272}$
- $\frac{180}{546}$
- $\frac{122}{274}$
- $\frac{58}{122}$
- $\frac{272}{546}$

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?

- $\frac{56}{546}$
- $\frac{86}{546}$
- $\frac{56}{274}$
- $\frac{86}{274}$
- $\frac{274}{546}$

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