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Two identical cube-shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:
- a)1/12
- b)1/8
- c)1/36
- d)1/4
Correct answer is option 'D'. Can you explain this answer?
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Two identical cube-shaped dice each with faces numbered 1 to 6 are ro...
Question Analysis:
We are given two identical cube-shaped dice, each with faces numbered 1 to 6. We need to find the probability that an even number is rolled on each dice.
Probability of rolling an even number:
Out of the six faces on the dice, three of them are even numbers (2, 4, and 6). So, the probability of rolling an even number on one dice is 3/6 or 1/2.
Probability of rolling an even number on both dice:
Since the two dice are identical, the probability of rolling an even number on the second dice is also 1/2.
Probability of independent events:
When two independent events occur, the probability of both events happening is the product of their individual probabilities.
Calculation:
The probability of rolling an even number on the first dice is 1/2, and the probability of rolling an even number on the second dice is also 1/2. So, the probability of both events happening is (1/2) * (1/2) = 1/4.
Conclusion:
The probability that an even number is rolled on each dice is 1/4. Therefore, the correct answer is option 'D'.
We are given two identical cube-shaped dice, each with faces numbered 1 to 6. We need to find the probability that an even number is rolled on each dice.
Probability of rolling an even number:
Out of the six faces on the dice, three of them are even numbers (2, 4, and 6). So, the probability of rolling an even number on one dice is 3/6 or 1/2.
Probability of rolling an even number on both dice:
Since the two dice are identical, the probability of rolling an even number on the second dice is also 1/2.
Probability of independent events:
When two independent events occur, the probability of both events happening is the product of their individual probabilities.
Calculation:
The probability of rolling an even number on the first dice is 1/2, and the probability of rolling an even number on the second dice is also 1/2. So, the probability of both events happening is (1/2) * (1/2) = 1/4.
Conclusion:
The probability that an even number is rolled on each dice is 1/4. Therefore, the correct answer is option 'D'.
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Community Answer
Two identical cube-shaped dice each with faces numbered 1 to 6 are ro...
Total number of events in sample space = 6 × 6 = 62 = 36
Number of favourable events of event A = 3 × 3 = 9
Required probability = 9/36 = 1/4
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Two identical cube-shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:a)1/12b)1/8c)1/36d)1/4Correct answer is option 'D'. Can you explain this answer?
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