Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Use the information below to determine the probability of each event occurring. Simplify if possible.

A die with sides numbered 1 to 6 is rolled. Find the probability of rolling each outcome.

5. [tex]P(5) = \qquad[/tex]

6. [tex]P(1 \text{ or } 2) = \qquad[/tex]

7. [tex]P(\text{odd number}) = \qquad[/tex]

8. [tex]P(\text{not } 6) = \qquad[/tex]

9. [tex]P(\text{even number}) = \qquad[/tex]

10. [tex]P(1, 2, 3, \text{ or } 4) = \qquad[/tex]

Sagot :

GinnyAnswer
To determine the probability of each specified event occurring when rolling a die with sides numbered 1 to 6, we need to analyze each scenario:

1. The probability of rolling a specific number (like 5):
[tex]\[ P(5) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
Since there is only one way to roll a 5, the probability is:
[tex]\[ P(5) = \frac{1}{6} \approx 0.1667 \][/tex]

2. The probability of rolling a 1 or a 2:
[tex]\[ P(1 \text{ or } 2) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
There are two favorable outcomes (rolling a 1 or a 2):
[tex]\[ P(1 \text{ or } 2) = \frac{2}{6} = \frac{1}{3} \approx 0.3333 \][/tex]

3. The probability of rolling an odd number (1, 3, 5):
[tex]\[ P(\text{odd number}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
There are three odd numbers on a die (1, 3, 5):
[tex]\[ P(\text{odd number}) = \frac{3}{6} = \frac{1}{2} = 0.5 \][/tex]

4. The probability of rolling a number that is not 6:
[tex]\[ P(\text{not 6}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
There are five favorable outcomes (1, 2, 3, 4, 5):
[tex]\[ P(\text{not 6}) = \frac{5}{6} \approx 0.8333 \][/tex]

5. The probability of rolling an even number (2, 4, 6):
[tex]\[ P(\text{even number}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
There are three even numbers on a die (2, 4, 6):
[tex]\[ P(\text{even number}) = \frac{3}{6} = \frac{1}{2} = 0.5 \][/tex]

6. The probability of rolling a 1, 2, 3, or 4:
[tex]\[ P(1, 2, 3, \text{ or } 4) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
There are four favorable outcomes (1, 2, 3, 4):
[tex]\[ P(1, 2, 3, \text{ or } 4) = \frac{4}{6} = \frac{2}{3} \approx 0.6667 \][/tex]

Summarizing the results:
1. [tex]\( P(5) \approx 0.1667 \)[/tex]
2. [tex]\( P(1 \text{ or } 2) \approx 0.3333 \)[/tex]
3. [tex]\( P(\text{odd number}) = 0.5 \)[/tex]
4. [tex]\( P(\text{not 6}) \approx 0.8333 \)[/tex]
5. [tex]\( P(\text{even number}) = 0.5 \)[/tex]
6. [tex]\( P(1, 2, 3, \text{ or } 4) \approx 0.6667 \)[/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.