Tree Diagrams & Counting Principle Quiz

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Questions and Answers

If a spinner has 4 sections with 3, 2, 4, and 1 outcome(s) respectively, what is the total number of outcomes?

11

A coin is flipped and a die is rolled. What is the probability that the coin lands on heads and the die shows an even number?

1/4

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, what is the probability that it is not blue?

7/10

A deck of cards has 52 cards, including 13 spades, 13 hearts, and 13 diamonds. What is the probability that a randomly drawn card is a spade or a heart?

<p>26/52</p>
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In a survey, 30 people chose coffee, 20 people chose tea, and 10 people chose neither. What is the probability that a randomly selected person chose tea or coffee?

<p>50/60</p>
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A box contains 5 shirts, 3 pairs of pants, and 2 hats. If one of each is chosen at random, how many outcomes are possible?

<p>30</p>
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What is the formula for the circumference of a circle?

<p>C = 2πr</p>
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A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 4 cm. What is its surface area?

<p>94 cm²</p>
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If a month is chosen at random from a year, what is the theoretical probability of choosing February or July?

<p>2/12 or 1/6</p>
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A blacksmith needs to create a handmade basketball hoop with a circumference of 36 inches. What is the radius of the hoop?

<p>r = 36 / (2π) = 5.73 inches</p>
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A rectangular prism has a volume of 120 cubic cm. If its length and width are 4 cm and 3 cm, respectively, what is its height?

<p>10 cm</p>
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If a month is chosen at random 300 times, how many times would you expect a month that ends with -ber to be chosen?

<p>25</p>
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Solve the inequality 6𝑦 − 10 ≥ 8 and graph your solution on the number line.

<p>Add 10 to both sides: 6𝑦 ≥ 18. Then divide both sides by 6: 𝑦 ≥ 3. The solution is all real numbers greater than or equal to 3.</p>
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Wesley worked for 32 hours last week and earned a total of $409.60. How much does he make per hour?

<p>To find the unit rate, divide the total amount earned ($409.60) by the number of hours worked (32). This gives $12.80 per hour.</p>
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Determine which option is the better deal: 6 granola bars for $6.48 or 5 granola bars for $5.50.

<p>Find the unit price for each option. For Option A, it is $6.48 ÷ 6 = $1.08 per granola bar. For Option B, it is $5.50 ÷ 5 = $1.10 per granola bar. Option A is the better deal.</p>
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The park and the movie theatre are 3.45 inches apart on a map. If the map has a scale of 0.25 inches = 5 miles, find the actual distance between the park and movie theatre.

<p>First, divide the scale by 0.25: 0.25 = 5, so 1 inch = 5/0.25 = 20 miles. Now, multiply the distance on the map (3.45 inches) by the scale: 3.45 × 20 = 69 miles.</p>
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Find 4% of 725.

<p>To find the percentage, multiply 725 by 0.04: 725 × 0.04 = 29.</p>
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Flashcards

What are total outcomes?

The total number of possible results from a random event.

What is probability of independent events?

Probability of one event AND another occurring.

What is circumference formula?

The formula to calculate the distance around a circle.

What is surface area?

Total area of all surfaces of a 3D object.

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What is theoretical probability?

Probability based on reasoning, not experiments.

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What is volume?

Space occupied by a 3D object.

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What is unit rate?

Finding the value for each single unit.

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What is map scale?

Ratio comparing map distance to actual distance.

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What is an inequality?

A mathematical statement showing greater than or less than.

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Radius of hoop with 36 inch circumference

A blacksmith needs to create a handmade basketball hoop with a circumference of 36 inches. What is the radius of the hoop?

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