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Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?
- a)1/336
- b)1/2
- c)17/28
- d)3/4
- e)301/336
Correct answer is option 'C'. Can you explain this answer?
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Set S is the set of all prime integers between 0 and 20. If three numb...
If set S is the set of all prime integers between 0 and 20 then: S = {2, 3, 5, 7, 11, 13, 17, 19}
Let’s start by finding the probability that the product of the three numbers chosenis a number less than 31. To keep the product less than 31, the three numbers must be 2, 3 and 5. So, what is the probability that the three numbers chosen will be some combination of 2, 3, and 5?
Here’s the list all possible combinations of 2, 3, and 5: case A: 2, 3, 5 case B: 2, 5, 3 case C: 3, 2, 5 case D: 3, 5, 2 case E: 5, 2, 3 case F: 5, 3, 2 This makes it easy to see that when 2 is chosen first, there are two possible combinations. The same is true when 3 and 5 are chosen first. The probability of drawing a 2, AND a 3, AND a 5 in case A is calculated as follows (remember, when calculating probabilities, AND means multiply): case A: (1/8) x (1/7) x (1/6) = 1/336 The same holds for the rest of the cases. case B: (1/8) x (1/7) x (1/6) = 1/336 case C: (1/8) x (1/7) x (1/6) = 1/336 case D: (1/8) x (1/7) x (1/6) = 1/336 case E: (1/8) x (1/7) x (1/6) = 1/336 case F: (1/8) x (1/7) x (1/6) = 1/336 So, a 2, 3, and 5 could be chosen according to case A, OR case B, OR, case C, etc. The total probability of getting a 2, 3, and 5, in any order, can be calculated as follows (remember, when calculating probabilities, OR means add): (1/336) + (1/336) + (1/336) + (1/336) + (1/336) + (1/336) = 6/336
Now, let’s calculate the probability that the sum of the three numbers is odd. In order to get an odd sum in this case, 2 must NOT be one of the numbers chosen. Using the rules of odds and evens, we can see that having a 2 would give the following scenario: even + odd + odd = even So, what is the probability that the three numbers chosen are all odd? We would need an odd AND another odd, AND another odd: (7/8) x (6/7) x (5/6) = 210/336 The positive difference between the two probabilities is: (210/336) – (6/336) = (204/336) = 17/28
Let’s start by finding the probability that the product of the three numbers chosenis a number less than 31. To keep the product less than 31, the three numbers must be 2, 3 and 5. So, what is the probability that the three numbers chosen will be some combination of 2, 3, and 5?
Here’s the list all possible combinations of 2, 3, and 5: case A: 2, 3, 5 case B: 2, 5, 3 case C: 3, 2, 5 case D: 3, 5, 2 case E: 5, 2, 3 case F: 5, 3, 2 This makes it easy to see that when 2 is chosen first, there are two possible combinations. The same is true when 3 and 5 are chosen first. The probability of drawing a 2, AND a 3, AND a 5 in case A is calculated as follows (remember, when calculating probabilities, AND means multiply): case A: (1/8) x (1/7) x (1/6) = 1/336 The same holds for the rest of the cases. case B: (1/8) x (1/7) x (1/6) = 1/336 case C: (1/8) x (1/7) x (1/6) = 1/336 case D: (1/8) x (1/7) x (1/6) = 1/336 case E: (1/8) x (1/7) x (1/6) = 1/336 case F: (1/8) x (1/7) x (1/6) = 1/336 So, a 2, 3, and 5 could be chosen according to case A, OR case B, OR, case C, etc. The total probability of getting a 2, 3, and 5, in any order, can be calculated as follows (remember, when calculating probabilities, OR means add): (1/336) + (1/336) + (1/336) + (1/336) + (1/336) + (1/336) = 6/336
Now, let’s calculate the probability that the sum of the three numbers is odd. In order to get an odd sum in this case, 2 must NOT be one of the numbers chosen. Using the rules of odds and evens, we can see that having a 2 would give the following scenario: even + odd + odd = even So, what is the probability that the three numbers chosen are all odd? We would need an odd AND another odd, AND another odd: (7/8) x (6/7) x (5/6) = 210/336 The positive difference between the two probabilities is: (210/336) – (6/336) = (204/336) = 17/28
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Set S is the set of all prime integers between 0 and 20. If three numb...
Problem Analysis:
- We are given a set S that contains all prime integers between 0 and 20.
- We need to find the positive difference between the probability that the product of three randomly chosen numbers from set S is less than 31 and the probability that the sum of three randomly chosen numbers from set S is odd.
Solution:
Step 1: Finding the number of elements in set S
- The set S contains all prime integers between 0 and 20.
- Prime numbers between 0 and 20 are: 2, 3, 5, 7, 11, 13, 17, 19.
- So, set S contains 8 elements.
Step 2: Finding the number of ways to choose 3 numbers from set S
- We need to choose 3 numbers from a set of 8 elements.
- The number of ways to choose k elements from a set of n elements is given by the combination formula: C(n, k) = n! / (k!(n-k)!)
- In this case, we need to find C(8, 3) = 8! / (3!(8-3)!) = 8! / (3!5!) = (8*7*6) / (3*2*1) = 8 * 7 * 6 / 6 = 8 * 7 = 56.
Step 3: Finding the number of ways to choose 3 numbers whose product is less than 31
- We need to find the number of ways to choose 3 numbers from set S such that their product is less than 31.
- To do this, we can analyze the possible combinations of 3 numbers from set S and find the ones that satisfy the condition.
- The prime numbers in set S are: 2, 3, 5, 7, 11, 13, 17, 19.
- Let's analyze each possible combination of 3 numbers:
- (2, 3, 5): Product = 2 * 3 * 5 = 30 (less than 31)
- (2, 3, 7): Product = 2 * 3 * 7 = 42 (greater than 31)
- (2, 3, 11): Product = 2 * 3 * 11 = 66 (greater than 31)
- (2, 3, 13): Product = 2 * 3 * 13 = 78 (greater than 31)
- (2, 3, 17): Product = 2 * 3 * 17 = 102 (greater than 31)
- (2, 3, 19): Product = 2 * 3 * 19 = 114 (greater than 31)
- (2, 5, 7): Product = 2 * 5 * 7 = 70 (greater than 31)
- (2, 5, 11): Product = 2 * 5 * 11 = 110 (greater than 31)
- (2, 5, 13): Product = 2 * 5 * 13 = 130 (greater than 31
- We are given a set S that contains all prime integers between 0 and 20.
- We need to find the positive difference between the probability that the product of three randomly chosen numbers from set S is less than 31 and the probability that the sum of three randomly chosen numbers from set S is odd.
Solution:
Step 1: Finding the number of elements in set S
- The set S contains all prime integers between 0 and 20.
- Prime numbers between 0 and 20 are: 2, 3, 5, 7, 11, 13, 17, 19.
- So, set S contains 8 elements.
Step 2: Finding the number of ways to choose 3 numbers from set S
- We need to choose 3 numbers from a set of 8 elements.
- The number of ways to choose k elements from a set of n elements is given by the combination formula: C(n, k) = n! / (k!(n-k)!)
- In this case, we need to find C(8, 3) = 8! / (3!(8-3)!) = 8! / (3!5!) = (8*7*6) / (3*2*1) = 8 * 7 * 6 / 6 = 8 * 7 = 56.
Step 3: Finding the number of ways to choose 3 numbers whose product is less than 31
- We need to find the number of ways to choose 3 numbers from set S such that their product is less than 31.
- To do this, we can analyze the possible combinations of 3 numbers from set S and find the ones that satisfy the condition.
- The prime numbers in set S are: 2, 3, 5, 7, 11, 13, 17, 19.
- Let's analyze each possible combination of 3 numbers:
- (2, 3, 5): Product = 2 * 3 * 5 = 30 (less than 31)
- (2, 3, 7): Product = 2 * 3 * 7 = 42 (greater than 31)
- (2, 3, 11): Product = 2 * 3 * 11 = 66 (greater than 31)
- (2, 3, 13): Product = 2 * 3 * 13 = 78 (greater than 31)
- (2, 3, 17): Product = 2 * 3 * 17 = 102 (greater than 31)
- (2, 3, 19): Product = 2 * 3 * 19 = 114 (greater than 31)
- (2, 5, 7): Product = 2 * 5 * 7 = 70 (greater than 31)
- (2, 5, 11): Product = 2 * 5 * 11 = 110 (greater than 31)
- (2, 5, 13): Product = 2 * 5 * 13 = 130 (greater than 31
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Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer?
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Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer?.
Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer?.
Solutions for Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?a)1/336b)1/2c)17/28d)3/4e)301/336Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
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