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Two dices are rolled simultaneously. The probability that the sum of digits on the top surface of the two dices is even, is
- a)0.5
- b)0.25
- c)0.167
- d)0.125
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two dices are rolled simultaneously. The probability that the sum of d...
Here sample space S= 6 × 6 = 36
Total no. of way in which sum of digits on the top surface of the two dice is is even is 18.
∴ The require probability = 0.5
Most Upvoted Answer
Two dices are rolled simultaneously. The probability that the sum of d...
To solve this problem, we need to determine the total number of outcomes where the sum of the digits on the top surface of the two dice is even, and then divide it by the total number of possible outcomes.
Let's consider the possible outcomes for each dice individually. Each dice has six sides, numbered from 1 to 6.
- Possible outcomes for the first dice: {1, 2, 3, 4, 5, 6}
- Possible outcomes for the second dice: {1, 2, 3, 4, 5, 6}
To find the total number of outcomes, we need to consider all possible combinations of the outcomes from both dice. Since there are 6 possible outcomes for each dice, the total number of outcomes is 6 x 6 = 36.
Now, let's determine the outcomes where the sum of the digits is even. There are three possible scenarios where the sum is even:
1. Both digits are even: There are three even digits on each dice (2, 4, and 6), so the number of outcomes where both digits are even is 3 x 3 = 9.
2. Both digits are odd: There are three odd digits on each dice (1, 3, and 5), so the number of outcomes where both digits are odd is 3 x 3 = 9.
3. One digit is even and the other is odd: There are three even digits and three odd digits on each dice, so the number of outcomes where one digit is even and the other is odd is 3 x 3 = 9.
Therefore, the total number of outcomes where the sum of the digits is even is 9 + 9 + 9 = 27.
Finally, we can calculate the probability by dividing the number of outcomes where the sum is even by the total number of possible outcomes:
Probability = Number of outcomes where sum is even / Total number of outcomes
Probability = 27 / 36
Probability = 0.75
Thus, the correct answer is option A) 0.5.
Let's consider the possible outcomes for each dice individually. Each dice has six sides, numbered from 1 to 6.
- Possible outcomes for the first dice: {1, 2, 3, 4, 5, 6}
- Possible outcomes for the second dice: {1, 2, 3, 4, 5, 6}
To find the total number of outcomes, we need to consider all possible combinations of the outcomes from both dice. Since there are 6 possible outcomes for each dice, the total number of outcomes is 6 x 6 = 36.
Now, let's determine the outcomes where the sum of the digits is even. There are three possible scenarios where the sum is even:
1. Both digits are even: There are three even digits on each dice (2, 4, and 6), so the number of outcomes where both digits are even is 3 x 3 = 9.
2. Both digits are odd: There are three odd digits on each dice (1, 3, and 5), so the number of outcomes where both digits are odd is 3 x 3 = 9.
3. One digit is even and the other is odd: There are three even digits and three odd digits on each dice, so the number of outcomes where one digit is even and the other is odd is 3 x 3 = 9.
Therefore, the total number of outcomes where the sum of the digits is even is 9 + 9 + 9 = 27.
Finally, we can calculate the probability by dividing the number of outcomes where the sum is even by the total number of possible outcomes:
Probability = Number of outcomes where sum is even / Total number of outcomes
Probability = 27 / 36
Probability = 0.75
Thus, the correct answer is option A) 0.5.
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Two dices are rolled simultaneously. The probability that the sum of digits on the top surface of the two dices is even, is a)0.5 b)0.25 c)0.167 d)0.125Correct answer is option 'A'. Can you explain this answer?
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Two dices are rolled simultaneously. The probability that the sum of digits on the top surface of the two dices is even, is a)0.5 b)0.25 c)0.167 d)0.125Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two dices are rolled simultaneously. The probability that the sum of digits on the top surface of the two dices is even, is a)0.5 b)0.25 c)0.167 d)0.125Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two dices are rolled simultaneously. The probability that the sum of digits on the top surface of the two dices is even, is a)0.5 b)0.25 c)0.167 d)0.125Correct answer is option 'A'. Can you explain this answer?.
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