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Two dices are numbered 1 2 3 4 5 6 and 122334 respectively they both are thrown and their sum of the numbers on them is noted find the probability of getting the sum of a perfect square?
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Two dices are numbered 1 2 3 4 5 6 and 122334 respectively they both a...
Understanding the Problem
When two dice are thrown, one with standard faces (1 to 6) and the other with faces numbered 1, 2, 2, 3, 3, 4, we need to find the probability that their sums yield a perfect square.
Identifying Perfect Squares
The perfect squares less than or equal to the maximum sum (6 + 4 = 10) are:
- 1
- 4
- 9
Therefore, the possible perfect square sums are 1, 4, and 9.
Calculating Possible Outcomes
The total outcomes when throwing both dice are:
- Standard die: 6 outcomes
- Unique die: 6 outcomes
Total outcomes = 6 * 6 = 36.
Finding Favorable Outcomes
Now, let’s find outcomes that yield perfect square sums:
- Sum = 4:
- (1, 3), (2, 2), (3, 1) → 3 outcomes
- Sum = 9:
- (5, 4), (6, 3) → 2 outcomes
Summing these outcomes gives us 5 favorable outcomes.
Calculating Probability
The probability of rolling a perfect square sum is calculated as:
- Probability = (Number of Favorable Outcomes) / (Total Outcomes)
- Probability = 5 / 36
Final Answer
The probability of getting a sum that is a perfect square when throwing both dice is 5/36.
When two dice are thrown, one with standard faces (1 to 6) and the other with faces numbered 1, 2, 2, 3, 3, 4, we need to find the probability that their sums yield a perfect square.
Identifying Perfect Squares
The perfect squares less than or equal to the maximum sum (6 + 4 = 10) are:
- 1
- 4
- 9
Therefore, the possible perfect square sums are 1, 4, and 9.
Calculating Possible Outcomes
The total outcomes when throwing both dice are:
- Standard die: 6 outcomes
- Unique die: 6 outcomes
Total outcomes = 6 * 6 = 36.
Finding Favorable Outcomes
Now, let’s find outcomes that yield perfect square sums:
- Sum = 4:
- (1, 3), (2, 2), (3, 1) → 3 outcomes
- Sum = 9:
- (5, 4), (6, 3) → 2 outcomes
Summing these outcomes gives us 5 favorable outcomes.
Calculating Probability
The probability of rolling a perfect square sum is calculated as:
- Probability = (Number of Favorable Outcomes) / (Total Outcomes)
- Probability = 5 / 36
Final Answer
The probability of getting a sum that is a perfect square when throwing both dice is 5/36.
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Two dices are numbered 1 2 3 4 5 6 and 122334 respectively they both are thrown and their sum of the numbers on them is noted find the probability of getting the sum of a perfect square?
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Two dices are numbered 1 2 3 4 5 6 and 122334 respectively they both are thrown and their sum of the numbers on them is noted find the probability of getting the sum of a perfect square? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two dices are numbered 1 2 3 4 5 6 and 122334 respectively they both are thrown and their sum of the numbers on them is noted find the probability of getting the sum of a perfect square? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two dices are numbered 1 2 3 4 5 6 and 122334 respectively they both are thrown and their sum of the numbers on them is noted find the probability of getting the sum of a perfect square?.
Two dices are numbered 1 2 3 4 5 6 and 122334 respectively they both are thrown and their sum of the numbers on them is noted find the probability of getting the sum of a perfect square? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two dices are numbered 1 2 3 4 5 6 and 122334 respectively they both are thrown and their sum of the numbers on them is noted find the probability of getting the sum of a perfect square? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two dices are numbered 1 2 3 4 5 6 and 122334 respectively they both are thrown and their sum of the numbers on them is noted find the probability of getting the sum of a perfect square?.
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