Problem: Probability of Various Dice Rolls
The task involves calculating the probabilities of different outcomes when rolling one or two six-sided dice. Let's solve each part step by step.
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1. Rolling a six-sided die and getting a 2
- A six-sided die has faces numbered
1, 2, 3, 4, 5, 6.
- There is only
1 favorable outcome (rolling a 2).
- The total number of possible outcomes is
6.
The probability is calculated as:
\[
P(\text{getting a 2}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6}
\]
Answer: \(\boxed{\frac{1}{6}}\)
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2. Rolling a six-sided die and getting a number less than 4
- The numbers less than 4 are
1, 2, 3.
- There are
3 favorable outcomes (rolling a 1, 2, or 3).
- The total number of possible outcomes is
6.
The probability is:
\[
P(\text{getting a number less than 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
Answer: \(\boxed{\frac{1}{2}}\)
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3. Rolling a six-sided die and getting a number over 2
- The numbers over 2 are
3, 4, 5, 6.
- There are
4 favorable outcomes (rolling a 3, 4, 5, or 6).
- The total number of possible outcomes is
6.
The probability is:
\[
P(\text{getting a number over 2}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{6} = \frac{2}{3}
\]
Answer: \(\boxed{\frac{2}{3}}\)
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4. Rolling a six-sided die and getting a 1 or a 5
- The favorable outcomes are
1 and 5.
- There are
2 favorable outcomes.
- The total number of possible outcomes is
6.
The probability is:
\[
P(\text{getting a 1 or a 5}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{2}{6} = \frac{1}{3}
\]
Answer: \(\boxed{\frac{1}{3}}\)
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5. Rolling two six-sided dice and getting a 7
- When rolling two six-sided dice, there are \(6 \times 6 = 36\) possible outcomes.
- The combinations that sum to 7 are:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
- There are
6 favorable outcomes.
The probability is:
\[
P(\text{getting a sum of 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{6}{36} = \frac{1}{6}
\]
Answer: \(\boxed{\frac{1}{6}}\)
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6. Rolling two six-sided dice and getting a 3 and a 6
- When rolling two six-sided dice, there are \(6 \times 6 = 36\) possible outcomes.
- The combinations that include a 3 and a 6 are:
- (3, 6)
- (6, 3)
- There are
2 favorable outcomes.
The probability is:
\[
P(\text{getting a 3 and a 6}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{2}{36} = \frac{1}{18}
\]
Answer: \(\boxed{\frac{1}{18}}\)
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Final Answers:
1. \(\boxed{\frac{1}{6}}\)
2. \(\boxed{\frac{1}{2}}\)
3. \(\boxed{\frac{2}{3}}\)
4. \(\boxed{\frac{1}{3}}\)
5. \(\boxed{\frac{1}{6}}\)
6. \(\boxed{\frac{1}{18}}\)
Parent Tip: Review the logic above to help your child master the concept of probability with dice worksheet.
