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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]
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