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If a is the set of all even numbers from 10 to 20 and b is the set of all prime numbers from 10 to 20 and see the element 15 then ab and c are mutually exclusive events or not explain how?
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If a is the set of all even numbers from 10 to 20 and b is the set of ...
Explanation:
Determining if events ab and c are mutually exclusive:
- Event ab represents the intersection of sets a and b, i.e., the even prime numbers in the range of 10 to 20.
- Event c represents the element 15, which is neither even nor prime.
Understanding mutually exclusive events:
- Two events are said to be mutually exclusive if they cannot occur at the same time.
- In other words, if one event happens, the other event cannot happen simultaneously.
Analysis:
- In this scenario, the elements of set a (even numbers) and set b (prime numbers) do not overlap.
- The set of even numbers from 10 to 20 is {10, 12, 14, 16, 18, 20}.
- The set of prime numbers from 10 to 20 is {11, 13, 17, 19}.
- The intersection of sets a and b (event ab) is an empty set as there are no numbers that are both even and prime in this range.
- Therefore, event ab and event c (element 15) are mutually exclusive because there is no common element between them.
Conclusion:
- Based on the analysis, it can be concluded that events ab and c are mutually exclusive in this scenario.
- This understanding is crucial in probability theory and helps in calculating the likelihood of various outcomes in different situations.
Determining if events ab and c are mutually exclusive:
- Event ab represents the intersection of sets a and b, i.e., the even prime numbers in the range of 10 to 20.
- Event c represents the element 15, which is neither even nor prime.
Understanding mutually exclusive events:
- Two events are said to be mutually exclusive if they cannot occur at the same time.
- In other words, if one event happens, the other event cannot happen simultaneously.
Analysis:
- In this scenario, the elements of set a (even numbers) and set b (prime numbers) do not overlap.
- The set of even numbers from 10 to 20 is {10, 12, 14, 16, 18, 20}.
- The set of prime numbers from 10 to 20 is {11, 13, 17, 19}.
- The intersection of sets a and b (event ab) is an empty set as there are no numbers that are both even and prime in this range.
- Therefore, event ab and event c (element 15) are mutually exclusive because there is no common element between them.
Conclusion:
- Based on the analysis, it can be concluded that events ab and c are mutually exclusive in this scenario.
- This understanding is crucial in probability theory and helps in calculating the likelihood of various outcomes in different situations.
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If a is the set of all even numbers from 10 to 20 and b is the set of all prime numbers from 10 to 20 and see the element 15 then ab and c are mutually exclusive events or not explain how?
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If a is the set of all even numbers from 10 to 20 and b is the set of all prime numbers from 10 to 20 and see the element 15 then ab and c are mutually exclusive events or not explain how? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If a is the set of all even numbers from 10 to 20 and b is the set of all prime numbers from 10 to 20 and see the element 15 then ab and c are mutually exclusive events or not explain how? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a is the set of all even numbers from 10 to 20 and b is the set of all prime numbers from 10 to 20 and see the element 15 then ab and c are mutually exclusive events or not explain how?.
If a is the set of all even numbers from 10 to 20 and b is the set of all prime numbers from 10 to 20 and see the element 15 then ab and c are mutually exclusive events or not explain how? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If a is the set of all even numbers from 10 to 20 and b is the set of all prime numbers from 10 to 20 and see the element 15 then ab and c are mutually exclusive events or not explain how? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a is the set of all even numbers from 10 to 20 and b is the set of all prime numbers from 10 to 20 and see the element 15 then ab and c are mutually exclusive events or not explain how?.
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