At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
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]
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]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
