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Which of the following set of function define a probability space on S = a1, a2, a3
- a)P(a1)= 1/3, P(a2) = ½, P(a3)= ¼
- b)P(a1)= 1/3, P(a2)= 1/6,P(a3)= ½
- c)P(a1)= P(a2)= 2/3, P(a3)= ¼
- d)None
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Which of the following set of function define a probability space on S...
Probability Space on S = a1, a2, a3
A probability space is a mathematical construct that defines a set of possible outcomes in an experiment, along with their associated probabilities. In this question, we are given a set S = {a1, a2, a3} and asked to determine which set of functions defines a probability space on S.
Option A: P(a1)= 1/3, P(a2) = , P(a3)=
This option is incomplete as the probability of a2 is not given. A probability space must assign probabilities to all possible outcomes in the sample space.
Option B: P(a1)= 1/3, P(a2)= 1/6, P(a3)=
This option defines a probability space on S as it assigns probabilities to all three outcomes in the sample space. The probabilities are:
- P(a1) = 1/3
- P(a2) = 1/6
- P(a3) = 1 - P(a1) - P(a2) = 1/2
The sum of these probabilities is 1, which is a requirement for a valid probability space.
Option C: P(a1)= P(a2)= 2/3, P(a3)=
This option violates the requirement that the sum of all probabilities must be 1. The sum of P(a1) and P(a2) is 4/3, which is greater than 1.
Option D: None
Option D is not a valid option as it does not define any set of functions.
Conclusion
Option B is the correct answer as it defines a valid probability space on S. Option A is incomplete, option C violates the sum of probabilities requirement, and option D is not a valid option.
A probability space is a mathematical construct that defines a set of possible outcomes in an experiment, along with their associated probabilities. In this question, we are given a set S = {a1, a2, a3} and asked to determine which set of functions defines a probability space on S.
Option A: P(a1)= 1/3, P(a2) = , P(a3)=
This option is incomplete as the probability of a2 is not given. A probability space must assign probabilities to all possible outcomes in the sample space.
Option B: P(a1)= 1/3, P(a2)= 1/6, P(a3)=
This option defines a probability space on S as it assigns probabilities to all three outcomes in the sample space. The probabilities are:
- P(a1) = 1/3
- P(a2) = 1/6
- P(a3) = 1 - P(a1) - P(a2) = 1/2
The sum of these probabilities is 1, which is a requirement for a valid probability space.
Option C: P(a1)= P(a2)= 2/3, P(a3)=
This option violates the requirement that the sum of all probabilities must be 1. The sum of P(a1) and P(a2) is 4/3, which is greater than 1.
Option D: None
Option D is not a valid option as it does not define any set of functions.
Conclusion
Option B is the correct answer as it defines a valid probability space on S. Option A is incomplete, option C violates the sum of probabilities requirement, and option D is not a valid option.
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Community Answer
Which of the following set of function define a probability space on S...
If we add q/3+1/6+1/2 it is equal to 1
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Which of the following set of function define a probability space on S = a1, a2, a3a)P(a1)= 1/3, P(a2) = ½, P(a3)= ¼b)P(a1)= 1/3, P(a2)= 1/6,P(a3)= ½c)P(a1)= P(a2)= 2/3, P(a3)= ¼d)NoneCorrect answer is option 'B'. Can you explain this answer?
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Which of the following set of function define a probability space on S = a1, a2, a3a)P(a1)= 1/3, P(a2) = ½, P(a3)= ¼b)P(a1)= 1/3, P(a2)= 1/6,P(a3)= ½c)P(a1)= P(a2)= 2/3, P(a3)= ¼d)NoneCorrect answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Which of the following set of function define a probability space on S = a1, a2, a3a)P(a1)= 1/3, P(a2) = ½, P(a3)= ¼b)P(a1)= 1/3, P(a2)= 1/6,P(a3)= ½c)P(a1)= P(a2)= 2/3, P(a3)= ¼d)NoneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following set of function define a probability space on S = a1, a2, a3a)P(a1)= 1/3, P(a2) = ½, P(a3)= ¼b)P(a1)= 1/3, P(a2)= 1/6,P(a3)= ½c)P(a1)= P(a2)= 2/3, P(a3)= ¼d)NoneCorrect answer is option 'B'. Can you explain this answer?.
Which of the following set of function define a probability space on S = a1, a2, a3a)P(a1)= 1/3, P(a2) = ½, P(a3)= ¼b)P(a1)= 1/3, P(a2)= 1/6,P(a3)= ½c)P(a1)= P(a2)= 2/3, P(a3)= ¼d)NoneCorrect answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Which of the following set of function define a probability space on S = a1, a2, a3a)P(a1)= 1/3, P(a2) = ½, P(a3)= ¼b)P(a1)= 1/3, P(a2)= 1/6,P(a3)= ½c)P(a1)= P(a2)= 2/3, P(a3)= ¼d)NoneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following set of function define a probability space on S = a1, a2, a3a)P(a1)= 1/3, P(a2) = ½, P(a3)= ¼b)P(a1)= 1/3, P(a2)= 1/6,P(a3)= ½c)P(a1)= P(a2)= 2/3, P(a3)= ¼d)NoneCorrect answer is option 'B'. Can you explain this answer?.
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