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Two unbaised dice are thrown. what is the probability that the first die is odd number and the other die is multiple of 2?
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Two unbaised dice are thrown. what is the probability that the first d...
Total Outcomes
To determine the probability, we first calculate the total number of possible outcomes when two unbiased dice are thrown. Each die has 6 sides, so:
- Total Outcomes = 6 (for the first die) × 6 (for the second die) = 36
Favorable Outcomes
Next, we identify the favorable outcomes where the first die shows an odd number, and the second die shows an even number (multiple of 2).
- Odd numbers on the first die: 1, 3, 5 (3 options)
- Even numbers on the second die: 2, 4, 6 (3 options)
Now, we calculate the total favorable outcomes:
- Favorable Outcomes = 3 (odd numbers) × 3 (even numbers) = 9
Probability Calculation
The probability (P) of the event occurring is calculated using the formula:
\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values:
\[ P = \frac{9}{36} = \frac{1}{4} \]
Conclusion
The probability that the first die shows an odd number and the second die shows a multiple of 2 is:
- Probability = 1/4 or 25%
This analysis provides a clear understanding of how to calculate the probability of specific outcomes when rolling two dice.
To determine the probability, we first calculate the total number of possible outcomes when two unbiased dice are thrown. Each die has 6 sides, so:
- Total Outcomes = 6 (for the first die) × 6 (for the second die) = 36
Favorable Outcomes
Next, we identify the favorable outcomes where the first die shows an odd number, and the second die shows an even number (multiple of 2).
- Odd numbers on the first die: 1, 3, 5 (3 options)
- Even numbers on the second die: 2, 4, 6 (3 options)
Now, we calculate the total favorable outcomes:
- Favorable Outcomes = 3 (odd numbers) × 3 (even numbers) = 9
Probability Calculation
The probability (P) of the event occurring is calculated using the formula:
\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values:
\[ P = \frac{9}{36} = \frac{1}{4} \]
Conclusion
The probability that the first die shows an odd number and the second die shows a multiple of 2 is:
- Probability = 1/4 or 25%
This analysis provides a clear understanding of how to calculate the probability of specific outcomes when rolling two dice.
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Two unbaised dice are thrown. what is the probability that the first die is odd number and the other die is multiple of 2?
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Two unbaised dice are thrown. what is the probability that the first die is odd number and the other die is multiple of 2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two unbaised dice are thrown. what is the probability that the first die is odd number and the other die is multiple of 2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two unbaised dice are thrown. what is the probability that the first die is odd number and the other die is multiple of 2?.
Two unbaised dice are thrown. what is the probability that the first die is odd number and the other die is multiple of 2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two unbaised dice are thrown. what is the probability that the first die is odd number and the other die is multiple of 2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two unbaised dice are thrown. what is the probability that the first die is odd number and the other die is multiple of 2?.
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