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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?
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There are two dice; red and green. What is the probability that on rol...
Probability of a Prime Number on the Red Die
To find the probability that the red die throws up a prime number, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Therefore, the favorable outcomes for the red die are the prime numbers: 2, 3, 5, 7.
Total Outcomes:
A standard die has 6 faces numbered from 1 to 6. Hence, the total number of outcomes for the red die is 6.
Probability of Prime Number on Red Die:
The probability of an event occurring is given by the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Using this formula, we can calculate the probability of the red die throwing up a prime number as follows:
Probability = (Number of favorable outcomes for red die) / (Total number of outcomes for red die)
Probability = 4 / 6
Probability = 2 / 3
Therefore, the probability of the red die throwing up a prime number is 2/3.
Probability of Divisibility by Green Die:
To find the probability that the number thrown up on the red die is divisible by the number thrown up on the green die, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
If the number thrown up on the green die is a prime number, then any prime number thrown up on the red die would be divisible by it. Therefore, the favorable outcomes for divisibility are the prime numbers: 2, 3, 5, 7.
Total Outcomes:
Similar to the red die, the green die also has 6 faces numbered from 1 to 6. Hence, the total number of outcomes for the green die is also 6.
Probability of Divisibility:
Using the formula for probability, we can calculate the probability of the number thrown up on the red die being divisible by the number thrown up on the green die as follows:
Probability = (Number of favorable outcomes for divisibility) / (Total number of outcomes for green die)
Probability = 4 / 6
Probability = 2 / 3
Therefore, the probability of the number thrown up on the red die being divisible by the number thrown up on the green die is 2/3.
Combined Probability:
Since the two events are independent, we can calculate the combined probability by multiplying the individual probabilities:
Combined Probability = Probability of prime number on red die * Probability of divisibility
Combined Probability = (2/3) * (2/3)
Combined Probability = 4/9
Therefore, the probability that on roll the red die throws up a prime number which is divisible by the number thrown up on the green die is 4/9.
To find the probability that the red die throws up a prime number, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Therefore, the favorable outcomes for the red die are the prime numbers: 2, 3, 5, 7.
Total Outcomes:
A standard die has 6 faces numbered from 1 to 6. Hence, the total number of outcomes for the red die is 6.
Probability of Prime Number on Red Die:
The probability of an event occurring is given by the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Using this formula, we can calculate the probability of the red die throwing up a prime number as follows:
Probability = (Number of favorable outcomes for red die) / (Total number of outcomes for red die)
Probability = 4 / 6
Probability = 2 / 3
Therefore, the probability of the red die throwing up a prime number is 2/3.
Probability of Divisibility by Green Die:
To find the probability that the number thrown up on the red die is divisible by the number thrown up on the green die, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
If the number thrown up on the green die is a prime number, then any prime number thrown up on the red die would be divisible by it. Therefore, the favorable outcomes for divisibility are the prime numbers: 2, 3, 5, 7.
Total Outcomes:
Similar to the red die, the green die also has 6 faces numbered from 1 to 6. Hence, the total number of outcomes for the green die is also 6.
Probability of Divisibility:
Using the formula for probability, we can calculate the probability of the number thrown up on the red die being divisible by the number thrown up on the green die as follows:
Probability = (Number of favorable outcomes for divisibility) / (Total number of outcomes for green die)
Probability = 4 / 6
Probability = 2 / 3
Therefore, the probability of the number thrown up on the red die being divisible by the number thrown up on the green die is 2/3.
Combined Probability:
Since the two events are independent, we can calculate the combined probability by multiplying the individual probabilities:
Combined Probability = Probability of prime number on red die * Probability of divisibility
Combined Probability = (2/3) * (2/3)
Combined Probability = 4/9
Therefore, the probability that on roll the red die throws up a prime number which is divisible by the number thrown up on the green die is 4/9.
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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?
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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? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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