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Two dice are thrown at the same time and the product of numbers appearing on them is noted the probability that the product of the number lies between 8 and 13 is?
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Two dice are thrown at the same time and the product of numbers appear...
- **Calculating the Sample Space:**
- When two dice are thrown, the sample space consists of all possible outcomes, which is \(6 \times 6 = 36\) outcomes.
- **Calculating the Favorable Outcomes:**
- To find the probability that the product of the numbers lies between 8 and 13, we need to determine the favorable outcomes.
- The pairs of numbers that result in a product between 8 and 13 are (2,4), (3,3), and (4,2).
- **Determining the Number of Favorable Outcomes:**
- The pairs (2,4) and (4,2) have 2 possible arrangements each, resulting in a total of 4 arrangements.
- The pair (3,3) has only 1 arrangement.
- Therefore, there are a total of 5 favorable outcomes.
- **Calculating the Probability:**
- The probability of the product of the numbers lying between 8 and 13 is given by:
\[
\text{{Probability}} = \frac{{\text{{Number of Favorable Outcomes}}}}{{\text{{Total Number of Outcomes}}}}
\]
\[
\text{{Probability}} = \frac{5}{36}
\]
- **Final Answer:**
- The probability that the product of the numbers lies between 8 and 13 when two dice are thrown simultaneously is \( \frac{5}{36} \).
- When two dice are thrown, the sample space consists of all possible outcomes, which is \(6 \times 6 = 36\) outcomes.
- **Calculating the Favorable Outcomes:**
- To find the probability that the product of the numbers lies between 8 and 13, we need to determine the favorable outcomes.
- The pairs of numbers that result in a product between 8 and 13 are (2,4), (3,3), and (4,2).
- **Determining the Number of Favorable Outcomes:**
- The pairs (2,4) and (4,2) have 2 possible arrangements each, resulting in a total of 4 arrangements.
- The pair (3,3) has only 1 arrangement.
- Therefore, there are a total of 5 favorable outcomes.
- **Calculating the Probability:**
- The probability of the product of the numbers lying between 8 and 13 is given by:
\[
\text{{Probability}} = \frac{{\text{{Number of Favorable Outcomes}}}}{{\text{{Total Number of Outcomes}}}}
\]
\[
\text{{Probability}} = \frac{5}{36}
\]
- **Final Answer:**
- The probability that the product of the numbers lies between 8 and 13 when two dice are thrown simultaneously is \( \frac{5}{36} \).
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Two dice are thrown at the same time and the product of numbers appearing on them is noted the probability that the product of the number lies between 8 and 13 is?
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Two dice are thrown at the same time and the product of numbers appearing on them is noted the probability that the product of the number lies between 8 and 13 is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two dice are thrown at the same time and the product of numbers appearing on them is noted the probability that the product of the number lies between 8 and 13 is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two dice are thrown at the same time and the product of numbers appearing on them is noted the probability that the product of the number lies between 8 and 13 is?.
Two dice are thrown at the same time and the product of numbers appearing on them is noted the probability that the product of the number lies between 8 and 13 is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two dice are thrown at the same time and the product of numbers appearing on them is noted the probability that the product of the number lies between 8 and 13 is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two dice are thrown at the same time and the product of numbers appearing on them is noted the probability that the product of the number lies between 8 and 13 is?.
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