Probability online exercise for Grade 8 - Free Printable

Problem Analysis and Solution

The worksheet focuses on calculating probabilities for simple events. Let's solve each question step by step.

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#### Activity 1

1. If you roll a number cube, what is the probability that you will roll an even number?

- A standard number cube has 6 faces: {1, 2, 3, 4, 5, 6}.
- Even numbers on the cube are: {2, 4, 6}.
- Total possible outcomes = 6.
- Favorable outcomes (even numbers) = 3.
- Probability = \(\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}\).

Answer: \(\frac{1}{2}\)

2. If you roll a number cube, what is the probability that you will roll a 9?

- A standard number cube has faces numbered from 1 to 6.
- The number 9 is not on the cube.
- Total possible outcomes = 6.
- Favorable outcomes (rolling a 9) = 0.
- Probability = \(\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{0}{6} = 0\).

Answer: \(0\)

3. From a standard deck of cards, what is the probability of picking a diamond?

- A standard deck has 52 cards.
- There are 4 suits: hearts, diamonds, clubs, and spades.
- Each suit has 13 cards.
- Total diamonds = 13.
- Total possible outcomes = 52.
- Favorable outcomes (diamonds) = 13.
- Probability = \(\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{13}{52} = \frac{1}{4}\).

Answer: \(\frac{1}{4}\)

4. From a standard deck of cards, what is the probability of picking a non-diamond?

- Total cards in the deck = 52.
- Total diamonds = 13.
- Non-diamond cards = 52 - 13 = 39.
- Total possible outcomes = 52.
- Favorable outcomes (non-diamonds) = 39.
- Probability = \(\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{39}{52} = \frac{3}{4}\).

Answer: \(\frac{3}{4}\)

5. Calculate the probability of each event.
- P(blue): The spinner is divided into 4 equal sections, with 2 blue sections.
- Total sections = 4.
- Blue sections = 2.
- Probability = \(\frac{\text{Blue sections}}{\text{Total sections}} = \frac{2}{4} = \frac{1}{2}\).
- P(not blue): The spinner has 2 yellow sections, which are not blue.
- Total sections = 4.
- Not blue sections = 2.
- Probability = \(\frac{\text{Not blue sections}}{\text{Total sections}} = \frac{2}{4} = \frac{1}{2}\).

Answers:
- P(blue) = \(\frac{1}{2}\)
- P(not blue) = \(\frac{1}{2}\)

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#### Activity 2

1. What is the probability that the wheel will stop on a yellow section?

- The spinner has 8 equal sections.
- Yellow sections = 2.
- Total sections = 8.
- Probability = \(\frac{\text{Yellow sections}}{\text{Total sections}} = \frac{2}{8} = \frac{1}{4}\).

Answer: \(\frac{1}{4}\)

2. What is the probability that the wheel will stop on an odd number (1, 3, 5, 7)?

- The spinner has numbers: {1, 2, 3, 4, 5, 6, 7, 8}.
- Odd numbers = {1, 3, 5, 7}.
- Total odd numbers = 4.
- Total sections = 8.
- Probability = \(\frac{\text{Odd numbers}}{\text{Total sections}} = \frac{4}{8} = \frac{1}{2}\).

Answer: \(\frac{1}{2}\)

3. What is the probability that the wheel will stop on a number greater than 2?

- Numbers greater than 2 = {3, 4, 5, 6, 7, 8}.
- Total numbers greater than 2 = 6.
- Total sections = 8.
- Probability = \(\frac{\text{Numbers > 2}}{\text{Total sections}} = \frac{6}{8} = \frac{3}{4}\).

Answer: \(\frac{3}{4}\)

4. What is the probability that the wheel will stop on a number less than 9?

- All numbers on the spinner are less than 9: {1, 2, 3, 4, 5, 6, 7, 8}.
- Total numbers less than 9 = 8.
- Total sections = 8.
- Probability = \(\frac{\text{Numbers < 9}}{\text{Total sections}} = \frac{8}{8} = 1\).

Answer: \(1\)

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Final Answers

#### Activity 1
1. \(\boxed{\frac{1}{2}}\)
2. \(\boxed{0}\)
3. \(\boxed{\frac{1}{4}}\)
4. \(\boxed{\frac{3}{4}}\)
5. P(blue) = \(\boxed{\frac{1}{2}}\), P(not blue) = \(\boxed{\frac{1}{2}}\)

#### Activity 2
1. \(\boxed{\frac{1}{4}}\)
2. \(\boxed{\frac{1}{2}}\)
3. \(\boxed{\frac{3}{4}}\)
4. \(\boxed{1}\)