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Two dice are thrown at random. What is the probability that the sum of the numbers that turn up on the dice is a prime number?
- a)1/6
- b)5/12
- c)7/18
- d)1/2
- e)3/4
Correct answer is option 'B'. Can you explain this answer?
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Two dice are thrown at random. What is the probability that the sum o...
The total score should be 2 or 3 or 5 or 7 or 11.
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The events where a prime sum is obtained on both the dice
Together is a prime number = {(1, 1), (1, 2), (2, 1), (2, 3), (3, 2), (1, 4), (4, 1), (3, 4), (4, 3), (2, 5),
(5, 2), (1, 6), (6, 1), (5, 6), (6, 5) }
i.e., 15 events
Therefore the required probability
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Two dice are thrown at random. What is the probability that the sum o...
Probability of the sum of the numbers being a prime number:
The sum of numbers on two dice can range from 2 to 12. To find the probability of the sum being a prime number, we need to first determine which sums are prime numbers.
Prime numbers less than or equal to 12:
- 2, 3, 5, 7, 11
Total possible outcomes when two dice are thrown:
Total outcomes = 6 * 6 = 36 (as each dice has 6 faces)
Favorable outcomes for prime sum:
- Sum of 2: only one possibility (1,1)
- Sum of 3: two possibilities (1,2) and (2,1)
- Sum of 5: four possibilities (1,4), (4,1), (2,3), (3,2)
- Sum of 7: six possibilities (1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
- Sum of 11: two possibilities (5,6), (6,5)
Total favorable outcomes:
Total favorable outcomes = 1 + 2 + 4 + 6 + 2 = 15
Probability of the sum being a prime number:
Probability = Favorable outcomes / Total outcomes
Probability = 15 / 36
Probability = 5/12
Therefore, the probability that the sum of the numbers turning up on the dice is a prime number is 5/12.
The sum of numbers on two dice can range from 2 to 12. To find the probability of the sum being a prime number, we need to first determine which sums are prime numbers.
Prime numbers less than or equal to 12:
- 2, 3, 5, 7, 11
Total possible outcomes when two dice are thrown:
Total outcomes = 6 * 6 = 36 (as each dice has 6 faces)
Favorable outcomes for prime sum:
- Sum of 2: only one possibility (1,1)
- Sum of 3: two possibilities (1,2) and (2,1)
- Sum of 5: four possibilities (1,4), (4,1), (2,3), (3,2)
- Sum of 7: six possibilities (1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
- Sum of 11: two possibilities (5,6), (6,5)
Total favorable outcomes:
Total favorable outcomes = 1 + 2 + 4 + 6 + 2 = 15
Probability of the sum being a prime number:
Probability = Favorable outcomes / Total outcomes
Probability = 15 / 36
Probability = 5/12
Therefore, the probability that the sum of the numbers turning up on the dice is a prime number is 5/12.
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Two dice are thrown at random. What is the probability that the sum of the numbers that turn up on the dice is a prime number?a)1/6b)5/12c)7/18d)1/2e)3/4Correct answer is option 'B'. Can you explain this answer?
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