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Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}.LetZ = (X+Y)..
What is P(Z is the product of two prime numbers) equal to ?
- a)0
- b)1/2
- c)1/4
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Number of X is randomly selected from the set of odd numbers and Y is ...
Set A = {1 ,2 ,3 ,4 ,5 ,6 ,7 } and z =x + y
x = set of odd numbers
y = set of even numbers
Z = product of two prime numbers
Z = x + y = 7 + 6 = 13
n(E4)=3
x = set of odd numbers
y = set of even numbers
Z = product of two prime numbers
Z = x + y = 7 + 6 = 13
n(E4)=3
Most Upvoted Answer
Number of X is randomly selected from the set of odd numbers and Y is ...
There are a few key points to consider in order to solve this problem:
1. Understanding the given sets: We are given two sets - the set of odd numbers {1, 3, 5, 7} and the set of even numbers {2, 4, 6}.
2. Selecting the numbers: We need to randomly select one number from each set. Let's consider the possible combinations:
- (1, 2)
- (1, 4)
- (1, 6)
- (3, 2)
- (3, 4)
- (3, 6)
- (5, 2)
- (5, 4)
- (5, 6)
- (7, 2)
- (7, 4)
- (7, 6)
3. Calculating the product: For each combination, we need to calculate the product of the two numbers. Let's calculate them:
- (1, 2) -> Z = 1 * 2 = 2
- (1, 4) -> Z = 1 * 4 = 4
- (1, 6) -> Z = 1 * 6 = 6
- (3, 2) -> Z = 3 * 2 = 6
- (3, 4) -> Z = 3 * 4 = 12
- (3, 6) -> Z = 3 * 6 = 18
- (5, 2) -> Z = 5 * 2 = 10
- (5, 4) -> Z = 5 * 4 = 20
- (5, 6) -> Z = 5 * 6 = 30
- (7, 2) -> Z = 7 * 2 = 14
- (7, 4) -> Z = 7 * 4 = 28
- (7, 6) -> Z = 7 * 6 = 42
4. Identifying the product of two prime numbers: From the calculated products, we can see that the following products are the product of two prime numbers:
- 2 (2 is a prime number)
- 3 (3 is a prime number)
- 5 (5 is a prime number)
- 7 (7 is a prime number)
- 11 (11 is a prime number)
- 13 (13 is a prime number)
- 17 (17 is a prime number)
- 19 (19 is a prime number)
- 23 (23 is a prime number)
- 29 (29 is a prime number)
- 31 (31 is a prime number)
5. Calculating the probability: Out of the total 12 possible combinations, there are 11 combinations where Z is the product of two prime numbers. Therefore, the probability of Z being the product of two prime numbers is 11/12, which is equal to 1/4.
Hence, the correct answer is option C) 1/4.
1. Understanding the given sets: We are given two sets - the set of odd numbers {1, 3, 5, 7} and the set of even numbers {2, 4, 6}.
2. Selecting the numbers: We need to randomly select one number from each set. Let's consider the possible combinations:
- (1, 2)
- (1, 4)
- (1, 6)
- (3, 2)
- (3, 4)
- (3, 6)
- (5, 2)
- (5, 4)
- (5, 6)
- (7, 2)
- (7, 4)
- (7, 6)
3. Calculating the product: For each combination, we need to calculate the product of the two numbers. Let's calculate them:
- (1, 2) -> Z = 1 * 2 = 2
- (1, 4) -> Z = 1 * 4 = 4
- (1, 6) -> Z = 1 * 6 = 6
- (3, 2) -> Z = 3 * 2 = 6
- (3, 4) -> Z = 3 * 4 = 12
- (3, 6) -> Z = 3 * 6 = 18
- (5, 2) -> Z = 5 * 2 = 10
- (5, 4) -> Z = 5 * 4 = 20
- (5, 6) -> Z = 5 * 6 = 30
- (7, 2) -> Z = 7 * 2 = 14
- (7, 4) -> Z = 7 * 4 = 28
- (7, 6) -> Z = 7 * 6 = 42
4. Identifying the product of two prime numbers: From the calculated products, we can see that the following products are the product of two prime numbers:
- 2 (2 is a prime number)
- 3 (3 is a prime number)
- 5 (5 is a prime number)
- 7 (7 is a prime number)
- 11 (11 is a prime number)
- 13 (13 is a prime number)
- 17 (17 is a prime number)
- 19 (19 is a prime number)
- 23 (23 is a prime number)
- 29 (29 is a prime number)
- 31 (31 is a prime number)
5. Calculating the probability: Out of the total 12 possible combinations, there are 11 combinations where Z is the product of two prime numbers. Therefore, the probability of Z being the product of two prime numbers is 11/12, which is equal to 1/4.
Hence, the correct answer is option C) 1/4.
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Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}.LetZ = (X+Y)..What is P(Z is the product of two prime numbers) equal to ?a)0b)1/2c)1/4d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}.LetZ = (X+Y)..What is P(Z is the product of two prime numbers) equal to ?a)0b)1/2c)1/4d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}.LetZ = (X+Y)..What is P(Z is the product of two prime numbers) equal to ?a)0b)1/2c)1/4d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}.LetZ = (X+Y)..What is P(Z is the product of two prime numbers) equal to ?a)0b)1/2c)1/4d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}.LetZ = (X+Y)..What is P(Z is the product of two prime numbers) equal to ?a)0b)1/2c)1/4d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}.LetZ = (X+Y)..What is P(Z is the product of two prime numbers) equal to ?a)0b)1/2c)1/4d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}.LetZ = (X+Y)..What is P(Z is the product of two prime numbers) equal to ?a)0b)1/2c)1/4d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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