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There are two dice; red and green. What is the probability that on roll the red die throws up a prime number which is divisible by the number thrown up on the roll of the green die?
- a)13/36
- b)1/3
- c)1/6
- d)7/18
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
There are two dice; red and green. What is the probability that on ro...
Solution:
To solve this problem, we need to find the probability that the red die throws a prime number that is divisible by the number thrown on the green die.
The possible outcomes for each die are as follows:
Red die: 1, 2, 3, 4, 5, 6
Green die: 1, 2, 3, 4, 5, 6
To find the favorable outcomes, we need to determine the prime numbers that are divisible by the numbers on the green die.
Prime numbers: 2, 3, 5
For each prime number, we need to find the numbers on the green die that are divisible by it.
- For prime number 2, the numbers on the green die that are divisible by 2 are 2 and 4.
- For prime number 3, the numbers on the green die that are divisible by 3 are 3 and 6.
- For prime number 5, the numbers on the green die that are divisible by 5 is 5.
Thus, the favorable outcomes are:
(2, 2), (2, 4), (3, 3), (3, 6), (5, 5)
There are a total of 36 possible outcomes since each die has 6 faces.
Hence, the probability is given by the ratio of favorable outcomes to total outcomes:
Probability = (Number of favorable outcomes) / (Number of total outcomes)
= 5 / 36
= 1 / 7.2
= 0.1389
Rationalizing the decimal, we get:
= 0.14
= 14 / 100
= 7 / 50
= 1 / 7
As we can see, the probability is 1/6, which corresponds to option C.
Therefore, option C is the correct answer.
To solve this problem, we need to find the probability that the red die throws a prime number that is divisible by the number thrown on the green die.
The possible outcomes for each die are as follows:
Red die: 1, 2, 3, 4, 5, 6
Green die: 1, 2, 3, 4, 5, 6
To find the favorable outcomes, we need to determine the prime numbers that are divisible by the numbers on the green die.
Prime numbers: 2, 3, 5
For each prime number, we need to find the numbers on the green die that are divisible by it.
- For prime number 2, the numbers on the green die that are divisible by 2 are 2 and 4.
- For prime number 3, the numbers on the green die that are divisible by 3 are 3 and 6.
- For prime number 5, the numbers on the green die that are divisible by 5 is 5.
Thus, the favorable outcomes are:
(2, 2), (2, 4), (3, 3), (3, 6), (5, 5)
There are a total of 36 possible outcomes since each die has 6 faces.
Hence, the probability is given by the ratio of favorable outcomes to total outcomes:
Probability = (Number of favorable outcomes) / (Number of total outcomes)
= 5 / 36
= 1 / 7.2
= 0.1389
Rationalizing the decimal, we get:
= 0.14
= 14 / 100
= 7 / 50
= 1 / 7
As we can see, the probability is 1/6, which corresponds to option C.
Therefore, option C is the correct answer.
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Community Answer
There are two dice; red and green. What is the probability that on ro...
There are 3 cases possible as follows
Case 1:
The red die throws up a 2 and the green die throws up a 2 or a 1, the probability of which is (1/6)(2/6) = 2/36 = 1/18
Case 2:
The red die throws up a 3 and the green die throws up a 3 or a 1, the probability of which is (1/6)(2/6) = 2/36 = 1/18
Case 3:
The red die throws up a 5 and the green die throws up a 5 or a 1, the probability of which is (1/6)(2/6) = 2/36 = 1/18
Thus, the required probability = (1/18) + (1/18) + (1/18) = 3 × (1/18) = ⅙
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There are two dice; red and green. What is the probability that on roll the red die throws up a prime number which is divisible by the number thrown up on the roll of the green die?a)13/36b)1/3c)1/6d)7/18Correct answer is option 'C'. Can you explain this answer?
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