Question

How many total different outcomes are possible when rolling two dice? Ways to roll a sum of 2 with two dice: Ways to roll a sum of 3 with two dice: Ways to roll a sum of 4 with two dice: Ways to roll a sum of 5 with two dice: Ways to roll a sum of 6 with two dice: Ways to roll a sum of 7 with two dice: Ways to roll a sum of 8 with two dice: Ways to roll a sum of 9 with two dice: Ways to roll a sum of 10 with two dice: Ways to roll a sum of 11 with two dice: Ways to roll a sum of 12 with two dice: Question 2 What is the probability of rolling a sum of 2 when rolling two dice. Show how to simplify all fractions. P(sum of 2) = ?(1 point) 10000 Word Limit Question 3 What is the probability of rolling a sum of 3 when rolling two dice. Show how to simplify all fractions. P(sum of 3) = ?(1 point) 0 / 10000 Word Limit Question 4 What is the probability of rolling a sum of 4 when rolling two dice. Show how to simplify all fractions. P(sum of 4) = ?(1 point) 0 / 10000 Word Limit Question 5 What is the probability of rolling a sum of 5 when rolling two dice. Show how to simplify all fractions. P(sum of 5) = ?(1 point) 0 / 10000 Word Limit Question 6 What is the probability of rolling a sum of 6 when rolling two dice. Show how to simplify all fractions. P(sum of 6) = ?(1 point) 0 / 10000 Word Limit Question 7 What is the probability of rolling a sum of 7 when rolling two dice. Show how to simplify all fractions. P(sum of 7) = ?(1 point) 0 / 10000 Word Limit Question 8 What is the probability of rolling a sum of 8 when rolling two dice. Show how to simplify all fractions. P(sum of 8) = ?(1 point) 0 / 10000 Word Limit Question 9 What is the probability of rolling a sum of 9 when rolling two dice. Show how to simplify all fractions. P(sum of 9) = ?(1 point) 0 / 10000 Word Limit Question 10 What is the probability of rolling a sum of 10 when rolling two dice. Show how to simplify all fractions. P(sum of 10) = ?(1 point) 0 / 10000 Word Limit Question 11 What is the probability of rolling a sum of 11 when rolling two dice. Show how to simplify all fractions. P(sum of 11) = ?(1 point) 0 / 10000 Word Limit Question 12 What is the probability of rolling a sum of 12 when rolling two dice. Show how to simplify all fractions. P(sum of 12) = ?(1 point) 0 / 10000 Word Limit Skip to navigation

Answer 1

Question 1: Total Outcomes and Sums

When rolling two six-sided dice, the total number of different outcomes is calculated by multiplying the number of outcomes for each die. Since each die has 6 faces, the total combinations are:

\[ \text{Total outcomes} = 6 \times 6 = 36 \]

Here’s the breakdown of the ways to roll sums from 2 to 12 with two dice:

• Ways to roll a sum of 2: (1, 1) → 1 way

• Ways to roll a sum of 3: (1, 2), (2, 1) → 2 ways

• Ways to roll a sum of 4: (1, 3), (2, 2), (3, 1) → 3 ways

• Ways to roll a sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) → 4 ways

• Ways to roll a sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) → 5 ways

• Ways to roll a sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) → 6 ways

• Ways to roll a sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) → 5 ways

• Ways to roll a sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) → 4 ways

• Ways to roll a sum of 10: (4, 6), (5, 5), (6, 4) → 3 ways

• Ways to roll a sum of 11: (5, 6), (6, 5) → 2 ways

• Ways to roll a sum of 12: (6, 6) → 1 way

Summarized Ways of Rolling Each Sum:

• Sum of 2: 1
• Sum of 3: 2
• Sum of 4: 3
• Sum of 5: 4
• Sum of 6: 5
• Sum of 7: 6
• Sum of 8: 5
• Sum of 9: 4
• Sum of 10: 3
• Sum of 11: 2
• Sum of 12: 1

Question 2: Probability of Rolling a Sum of 2

The probability \( P \) of rolling a sum of 2 is calculated as follows:

\[ P(\text{sum of 2}) = \frac{\text{Number of ways to roll a sum of 2}}{\text{Total outcomes}} = \frac{1}{36} \]

Question 3: Probability of Rolling a Sum of 3

\[ P(\text{sum of 3}) = \frac{\text{Number of ways to roll a sum of 3}}{\text{Total outcomes}} = \frac{2}{36} = \frac{1}{18} \]

Question 4: Probability of Rolling a Sum of 4

\[ P(\text{sum of 4}) = \frac{\text{Number of ways to roll a sum of 4}}{\text{Total outcomes}} = \frac{3}{36} = \frac{1}{12} \]

Question 5: Probability of Rolling a Sum of 5

\[ P(\text{sum of 5}) = \frac{\text{Number of ways to roll a sum of 5}}{\text{Total outcomes}} = \frac{4}{36} = \frac{1}{9} \]

Question 6: Probability of Rolling a Sum of 6

\[ P(\text{sum of 6}) = \frac{\text{Number of ways to roll a sum of 6}}{\text{Total outcomes}} = \frac{5}{36} \]

Question 7: Probability of Rolling a Sum of 7

\[ P(\text{sum of 7}) = \frac{\text{Number of ways to roll a sum of 7}}{\text{Total outcomes}} = \frac{6}{36} = \frac{1}{6} \]

Question 8: Probability of Rolling a Sum of 8

\[ P(\text{sum of 8}) = \frac{\text{Number of ways to roll a sum of 8}}{\text{Total outcomes}} = \frac{5}{36} \]

Question 9: Probability of Rolling a Sum of 9

\[ P(\text{sum of 9}) = \frac{\text{Number of ways to roll a sum of 9}}{\text{Total outcomes}} = \frac{4}{36} = \frac{1}{9} \]

Question 10: Probability of Rolling a Sum of 10

\[ P(\text{sum of 10}) = \frac{\text{Number of ways to roll a sum of 10}}{\text{Total outcomes}} = \frac{3}{36} = \frac{1}{12} \]

Question 11: Probability of Rolling a Sum of 11

\[ P(\text{sum of 11}) = \frac{\text{Number of ways to roll a sum of 11}}{\text{Total outcomes}} = \frac{2}{36} = \frac{1}{18} \]

Question 12: Probability of Rolling a Sum of 12

\[ P(\text{sum of 12}) = \frac{\text{Number of ways to roll a sum of 12}}{\text{Total outcomes}} = \frac{1}{36} \]

Summary of Probabilities

• \( P(\text{sum of 2}) = \frac{1}{36} \)
• \( P(\text{sum of 3}) = \frac{1}{18} \)
• \( P(\text{sum of 4}) = \frac{1}{12} \)
• \( P(\text{sum of 5}) = \frac{1}{9} \)
• \( P(\text{sum of 6}) = \frac{5}{36} \)
• \( P(\text{sum of 7}) = \frac{1}{6} \)
• \( P(\text{sum of 8}) = \frac{5}{36} \)
• \( P(\text{sum of 9}) = \frac{1}{9} \)
• \( P(\text{sum of 10}) = \frac{1}{12} \)
• \( P(\text{sum of 11}) = \frac{1}{18} \)
• \( P(\text{sum of 12}) = \frac{1}{36} \)