Let's solve each probability problem step by step based on the image you provided. The image is about calculating probabilities related to rolling dice.
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Reminder:
> Probability is the chance that something will happen.
> It is calculated as:
> $$
> \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
> $$
We'll use this formula for all problems.
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1) Rolling a six-sided die and getting a 2?
- A standard six-sided die has numbers: 1, 2, 3, 4, 5, 6 → Total outcomes = 6
- Favorable outcome (rolling a 2) = 1
$$
\text{Probability} = \frac{1}{6}
$$
✔ Answer: $ \frac{1}{6} $
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2) Rolling a six-sided die and getting a number less than 4?
- Numbers less than 4: 1, 2, 3 → 3 favorable outcomes
- Total outcomes = 6
$$
\text{Probability} = \frac{3}{6} = \frac{1}{2}
$$
✔ Answer: $ \frac{1}{2} $
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3) Rolling a six-sided die and getting a number over 2?
- Numbers over 2: 3, 4, 5, 6 → 4 favorable outcomes
- Total outcomes = 6
$$
\text{Probability} = \frac{4}{6} = \frac{2}{3}
$$
✔ Answer: $ \frac{2}{3} $
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4) Rolling a six-sided die and getting a 1 or a 5?
- Favorable outcomes: 1 or 5 → 2 outcomes
- Total outcomes = 6
$$
\text{Probability} = \frac{2}{6} = \frac{1}{3}
$$
✔ Answer: $ \frac{1}{3} $
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5) Rolling two six-sided dice and getting a 5?
Now we are rolling
two dice. Each die has 6 sides, so total possible outcomes:
$$
6 \times 6 = 36
$$
We want the
sum to be 5.
List the combinations that give a sum of 5:
- (1,4)
- (2,3)
- (3,2)
- (4,1)
→ 4 favorable outcomes
$$
\text{Probability} = \frac{4}{36} = \frac{1}{9}
$$
✔ Answer: $ \frac{1}{9} $
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6) Rolling two six-sided dice and getting a 3 and a 6?
This means one die shows 3 and the other shows 6.
Possible combinations:
- (3,6)
- (6,3)
→ 2 favorable outcomes
Total outcomes = 36
$$
\text{Probability} = \frac{2}{36} = \frac{1}{18}
$$
✔ Answer: $ \frac{1}{18} $
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✔ Final Answers:
1. $ \frac{1}{6} $
2. $ \frac{1}{2} $
3. $ \frac{2}{3} $
4. $ \frac{1}{3} $
5. $ \frac{1}{9} $
6. $ \frac{1}{18} $
Let me know if you'd like these shown as decimals or percentages too!
Parent Tip: Review the logic above to help your child master the concept of dice probability worksheet.
