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In a biased dice with numbers from 1 to 6, each prime number has an equal chance of showing up and each non-prime number has an equal chance of showing up on a roll of the dice. If the probability that an odd number is rolled is 4/9, what is the probability that 6 is rolled in ane throw of the dice?
- a)1/6
- b)1/9
- c)1/3
- d)2/9
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a biased dice with numbers from 1 to 6, each prime number has an eq...
Let P(2) = P(3) = P(5) = x
and let P(1) = P(4) = P(6) = y
Now, we know the probability of an odd number is 4/9.
2x + y = 4/9 or 18x + 9y = 4
Also, total probability is 1.
Hence, 3x+3y = 1
x + y = 1/3
Solving the 2 equations, we get x = 1/9 and y = 2/9.
Hence, probability of getting a six = 2/9
and let P(1) = P(4) = P(6) = y
Now, we know the probability of an odd number is 4/9.
2x + y = 4/9 or 18x + 9y = 4
Also, total probability is 1.
Hence, 3x+3y = 1
x + y = 1/3
Solving the 2 equations, we get x = 1/9 and y = 2/9.
Hence, probability of getting a six = 2/9
Most Upvoted Answer
In a biased dice with numbers from 1 to 6, each prime number has an eq...
To solve this problem, we need to determine the probability of rolling a 6 on the biased dice. Let's break down the problem step by step:
Step 1: Understanding the given information
We are told that the dice is biased, meaning that certain numbers have a higher chance of showing up than others. Specifically, prime numbers and non-prime numbers have equal chances of appearing.
Step 2: Analyzing the probability of odd numbers
We are given that the probability of rolling an odd number is 4/9. Since there are three odd numbers (1, 3, and 5) on the dice, and the sum of their probabilities should be 4/9, we can conclude that each odd number has a probability of 4/27 (4/9 divided by 3).
Step 3: Calculating the probability of rolling a 6
Now, let's calculate the probability of rolling a 6. Since 6 is not an odd number, it must be a non-prime number. We are told that non-prime numbers have an equal chance of showing up, so each non-prime number should have a probability of (4/9)/3 = 4/27.
Since 6 is one of the non-prime numbers on the dice, the probability of rolling a 6 is 4/27.
Step 4: Identifying the correct answer
Now that we have calculated the probability of rolling a 6 as 4/27, we need to identify the corresponding option among the given choices. The correct answer is option D, 2/9.
In summary, the probability of rolling a 6 on the biased dice is 4/27, which corresponds to option D.
Step 1: Understanding the given information
We are told that the dice is biased, meaning that certain numbers have a higher chance of showing up than others. Specifically, prime numbers and non-prime numbers have equal chances of appearing.
Step 2: Analyzing the probability of odd numbers
We are given that the probability of rolling an odd number is 4/9. Since there are three odd numbers (1, 3, and 5) on the dice, and the sum of their probabilities should be 4/9, we can conclude that each odd number has a probability of 4/27 (4/9 divided by 3).
Step 3: Calculating the probability of rolling a 6
Now, let's calculate the probability of rolling a 6. Since 6 is not an odd number, it must be a non-prime number. We are told that non-prime numbers have an equal chance of showing up, so each non-prime number should have a probability of (4/9)/3 = 4/27.
Since 6 is one of the non-prime numbers on the dice, the probability of rolling a 6 is 4/27.
Step 4: Identifying the correct answer
Now that we have calculated the probability of rolling a 6 as 4/27, we need to identify the corresponding option among the given choices. The correct answer is option D, 2/9.
In summary, the probability of rolling a 6 on the biased dice is 4/27, which corresponds to option D.
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In a biased dice with numbers from 1 to 6, each prime number has an equal chance of showing up and each non-prime number has an equal chance of showing up on a roll of the dice. If the probability that an odd number is rolled is 4/9, what is the probability that 6 is rolled in ane throw of the dice?a)1/6b)1/9c)1/3d)2/9Correct answer is option 'D'. Can you explain this answer?
Question Description
In a biased dice with numbers from 1 to 6, each prime number has an equal chance of showing up and each non-prime number has an equal chance of showing up on a roll of the dice. If the probability that an odd number is rolled is 4/9, what is the probability that 6 is rolled in ane throw of the dice?a)1/6b)1/9c)1/3d)2/9Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a biased dice with numbers from 1 to 6, each prime number has an equal chance of showing up and each non-prime number has an equal chance of showing up on a roll of the dice. If the probability that an odd number is rolled is 4/9, what is the probability that 6 is rolled in ane throw of the dice?a)1/6b)1/9c)1/3d)2/9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a biased dice with numbers from 1 to 6, each prime number has an equal chance of showing up and each non-prime number has an equal chance of showing up on a roll of the dice. If the probability that an odd number is rolled is 4/9, what is the probability that 6 is rolled in ane throw of the dice?a)1/6b)1/9c)1/3d)2/9Correct answer is option 'D'. Can you explain this answer?.
In a biased dice with numbers from 1 to 6, each prime number has an equal chance of showing up and each non-prime number has an equal chance of showing up on a roll of the dice. If the probability that an odd number is rolled is 4/9, what is the probability that 6 is rolled in ane throw of the dice?a)1/6b)1/9c)1/3d)2/9Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a biased dice with numbers from 1 to 6, each prime number has an equal chance of showing up and each non-prime number has an equal chance of showing up on a roll of the dice. If the probability that an odd number is rolled is 4/9, what is the probability that 6 is rolled in ane throw of the dice?a)1/6b)1/9c)1/3d)2/9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a biased dice with numbers from 1 to 6, each prime number has an equal chance of showing up and each non-prime number has an equal chance of showing up on a roll of the dice. If the probability that an odd number is rolled is 4/9, what is the probability that 6 is rolled in ane throw of the dice?a)1/6b)1/9c)1/3d)2/9Correct answer is option 'D'. Can you explain this answer?.
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