A fair die ( 6 sided) is rolled. Express the answers in simplest fraction form.
P(even *) =
multiples of 2
odd
multiples of 4
or 3

or higher

Ask by Frazier Dawson. in the United States

Jan 22,2025

Question

A fair die ( 6 sided) is rolled. Express the answers in simplest fraction form.
P(even *) =
multiples of 2
odd
multiples of 4
or 3

or higher

Ask by Frazier Dawson. in the United States

Jan 22,2025

UpStudy AI · Accepted Answer

Let's analyze each probability for a fair 6-sided die with outcomes $$ \{1, 2, 3, 4, 5, 6\} $$. Each outcome has an equal probability of $$ \frac{1}{6} $$.

1. **$$ P(\text{even}) $$**
   
   **Even numbers:** 2, 4, 6
   
   $$
   P(\text{even}) = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
   $$

2. **$$ P(\text{multiples of 2}) $$**
   
   Multiples of 2 are the even numbers: 2, 4, 6
   
   $$
   P(\text{multiples of 2}) = \frac{3}{6} = \frac{1}{2}
   $$

3. **$$ P(\text{odd}) $$**
   
   **Odd numbers:** 1, 3, 5
   
   $$
   P(\text{odd}) = \frac{3}{6} = \frac{1}{2}
   $$

4. **$$ P(\text{multiples of 4}) $$**
   
   **Multiples of 4:** 4
   
   $$
   P(\text{multiples of 4}) = \frac{1}{6}
   $$

5. **$$ P(2 \text{ or } 3) $$**
   
   **Favorable outcomes:** 2, 3
   
   $$
   P(2 \text{ or } 3) = \frac{2}{6} = \frac{1}{3}
   $$

6. **$$ P(7) $$**
   
   Since a 6-sided die only has numbers up to 6, getting a 7 is impossible.
   
   $$
   P(7) = 0
   $$

7. **$$ P(5) $$**
   
   **Favorable outcome:** 5
   
   $$
   P(5) = \frac{1}{6}
   $$

8. **$$ P(2 \text{ or higher}) $$**
   
   **Outcomes 2 or higher:** 2, 3, 4, 5, 6
   
   $$
   P(2 \text{ or higher}) = \frac{5}{6}
   $$

### Summary of Probabilities

- $$ P(\text{even}) = \frac{1}{2} $$
- $$ P(\text{multiples of 2}) = \frac{1}{2} $$
- $$ P(\text{odd}) = \frac{1}{2} $$
- $$ P(\text{multiples of 4}) = \frac{1}{6} $$
- $$ P(2 \text{ or } 3) = \frac{1}{3} $$
- $$ P(7) = 0 $$
- $$ P(5) = \frac{1}{6} $$
- $$ P(2 \text{ or higher}) = \frac{5}{6} $$
- $$ P(\text{even}) = \frac{1}{2} $$ - $$ P(\text{multiples of 2}) = \frac{1}{2} $$ - $$ P(\text{odd}) = \frac{1}{2} $$ - $$ P(\text{multiples of 4}) = \frac{1}{6} $$ - $$ P(2 \text{ or } 3) = \frac{1}{3} $$ - $$ P(7) = 0 $$ - $$ P(5) = \frac{1}{6} $$ - $$ P(2 \text{ or higher}) = \frac{5}{6} $$

A fair die ( 6 sided) is rolled. Express the answers in simplest fraction form.
P(even *) =
multiples of 2
odd
multiples of 4
or 3

or higher

Upstudy AI Solution

Answer

Solution

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A fair die ( 6 sided) is rolled. Express the answers in simplest fraction form. P(even *) = multiples of 2 odd multiples of 4 or 3 or higher

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A fair die ( 6 sided) is rolled. Express the answers in simplest fraction form.
P(even *) =
multiples of 2
odd
multiples of 4
or 3

or higher