# Lesson 4

Tables of Relative Frequencies

- Let’s use tables to organize probabilities.

### Problem 1

The table shows the results from a survey that asked 100 adults if they had a high school diploma and if their annual income was more than $30,000.

$30,000 or less | more than $30,000 | |
---|---|---|

high school diploma | 21 | 68 |

no high school diploma | 9 | 2 |

A person who took the survey is selected at random.

- What is the probability that the person has a high school diploma and makes $30,000 or less?
- What is the probability that the person has no high school diploma and earns more than $30,000?

### Problem 2

The table shows data from a science fair experiment that studied the number of eggs that hatched at three different temperatures.

cool | room temperature | warm | |
---|---|---|---|

hatched | 6 | 14 | 23 |

not hatched | 19 | 11 | 2 |

- What percentage of the eggs hatched?
- What percentage of the eggs that were at the cool temperature hatched?
- What percentage of the eggs were not at room temperature?
- What percentage of the eggs were at the warm temperature and did not hatch?

### Problem 3

The table shows information from a survey about the resting heart rate in beats per minute (bpm), for 50 people living at altitudes above and below 10,000 feet.

below 80 bpm | above 80 bpm | total | |
---|---|---|---|

above 10,000 ft | 3 | 19 | 22 |

10,000 ft or below | 16 | 12 | 28 |

total | 19 | 31 | 50 |

- Create a two-way table that shows the relative frequency for each of the values in the table relative to all 50 people in the survey.
- What is the probability that a person surveyed, selected at random, has a heart rate above 80 bpm or lives above 10,000 ft?
- What is the probability that a person surveyed, selected at random, has a heart rate above 80 bpm and lives above 10,000 ft?

### Problem 4

List all the possible outcomes for spinning the spinner and rolling a fair number cube.

### Problem 5

A student flips a fair coin and then spins this spinner. How would you find the sample space?

### Problem 6

Select **all** of the words for which the probability of selecting the letter A at random is \(\frac{1}{4}\)

AREA

ACID

ANGRY

APPEASED

AARDVARK

### Problem 7

On an assignment, there are two multiple choice questions with four answers choices each. You have no idea what the correct answer is to either one so you guess.

- What is the probability that you get both of them right by guessing? Explain your answer.
- What is the probability that you get exactly one of them right by guessing? Explain your answer.

### Problem 8

Here are 2 circles. The smaller circle has radius \(r\), circumference \(c\), and diameter \(d\). The larger circle has radius \(R\), circumference \(C\), and diameter \(D\). The larger circle is a dilation of the smaller circle by a factor of \(k\).

Using the circles, match the pairs of ratios with their values.