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Let a sample space be S = {X1, X2, X3} which of the fallowing defines probability space on S ?
- a)P(X1)= ¼ , P(X2)= 1/3 , P(X3)= 1/3
- b)P(X1)= 0, P(X2)= 1/3, P(X3)= 2/3
- c)P(X1)= 2/3 , P(X2)= 1/3 , P(X3)= 2/3
- d)none
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Let a sample space be S = {X1, X2, X3} which of the fallowing defines ...
Solution:
Defining a probability space involves assigning probabilities to each outcome in the sample space. In this case, the sample space S has three outcomes: X1, X2, and X3.
To define a probability space, we need to assign probabilities to each outcome such that:
- The probabilities are non-negative (i.e., greater than or equal to 0).
- The sum of the probabilities is 1 (i.e., all possible outcomes must have a total probability of 1).
Let's consider each option one by one:
a) P(X1) = ?, P(X2) = 1/3, P(X3) = 1/3
- The probability assigned to X1 is missing, so we cannot say whether this option defines a probability space or not.
- The probabilities assigned to X2 and X3 are both positive and add up to 2/3, which is less than 1. Therefore, this option does not define a probability space.
b) P(X1) = 0, P(X2) = 1/3, P(X3) = 2/3
- The probability assigned to X1 is 0, which is non-negative.
- The probabilities assigned to X2 and X3 are both positive and add up to 1, which is the total probability of all possible outcomes. Therefore, this option defines a probability space.
c) P(X1) = 2/3, P(X2) = 1/3, P(X3) = 2/3
- The probabilities assigned to X1 and X3 are both greater than 1/2, which violates the rule that probabilities must be less than or equal to 1.
- Therefore, this option does not define a probability space.
d) None
- This option does not define a probability space.
Therefore, the correct answer is option B, which assigns probabilities such that the sum is 1 and all probabilities are non-negative.
Defining a probability space involves assigning probabilities to each outcome in the sample space. In this case, the sample space S has three outcomes: X1, X2, and X3.
To define a probability space, we need to assign probabilities to each outcome such that:
- The probabilities are non-negative (i.e., greater than or equal to 0).
- The sum of the probabilities is 1 (i.e., all possible outcomes must have a total probability of 1).
Let's consider each option one by one:
a) P(X1) = ?, P(X2) = 1/3, P(X3) = 1/3
- The probability assigned to X1 is missing, so we cannot say whether this option defines a probability space or not.
- The probabilities assigned to X2 and X3 are both positive and add up to 2/3, which is less than 1. Therefore, this option does not define a probability space.
b) P(X1) = 0, P(X2) = 1/3, P(X3) = 2/3
- The probability assigned to X1 is 0, which is non-negative.
- The probabilities assigned to X2 and X3 are both positive and add up to 1, which is the total probability of all possible outcomes. Therefore, this option defines a probability space.
c) P(X1) = 2/3, P(X2) = 1/3, P(X3) = 2/3
- The probabilities assigned to X1 and X3 are both greater than 1/2, which violates the rule that probabilities must be less than or equal to 1.
- Therefore, this option does not define a probability space.
d) None
- This option does not define a probability space.
Therefore, the correct answer is option B, which assigns probabilities such that the sum is 1 and all probabilities are non-negative.
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Community Answer
Let a sample space be S = {X1, X2, X3} which of the fallowing defines ...
The sum of the probability of a sample space should be equal to 1.
Therefore, in option B 1/3+2/3+0=1
Hence, the correct option is B.
Therefore, in option B 1/3+2/3+0=1
Hence, the correct option is B.
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Let a sample space be S = {X1, X2, X3} which of the fallowing defines probability space on S ?a)P(X1)= ¼ , P(X2)= 1/3 , P(X3)= 1/3b)P(X1)= 0, P(X2)= 1/3, P(X3)= 2/3c)P(X1)= 2/3 , P(X2)= 1/3 , P(X3)= 2/3d)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 Let a sample space be S = {X1, X2, X3} which of the fallowing defines probability space on S ?a)P(X1)= ¼ , P(X2)= 1/3 , P(X3)= 1/3b)P(X1)= 0, P(X2)= 1/3, P(X3)= 2/3c)P(X1)= 2/3 , P(X2)= 1/3 , P(X3)= 2/3d)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 Let a sample space be S = {X1, X2, X3} which of the fallowing defines probability space on S ?a)P(X1)= ¼ , P(X2)= 1/3 , P(X3)= 1/3b)P(X1)= 0, P(X2)= 1/3, P(X3)= 2/3c)P(X1)= 2/3 , P(X2)= 1/3 , P(X3)= 2/3d)noneCorrect answer is option 'B'. Can you explain this answer?.
Let a sample space be S = {X1, X2, X3} which of the fallowing defines probability space on S ?a)P(X1)= ¼ , P(X2)= 1/3 , P(X3)= 1/3b)P(X1)= 0, P(X2)= 1/3, P(X3)= 2/3c)P(X1)= 2/3 , P(X2)= 1/3 , P(X3)= 2/3d)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 Let a sample space be S = {X1, X2, X3} which of the fallowing defines probability space on S ?a)P(X1)= ¼ , P(X2)= 1/3 , P(X3)= 1/3b)P(X1)= 0, P(X2)= 1/3, P(X3)= 2/3c)P(X1)= 2/3 , P(X2)= 1/3 , P(X3)= 2/3d)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 Let a sample space be S = {X1, X2, X3} which of the fallowing defines probability space on S ?a)P(X1)= ¼ , P(X2)= 1/3 , P(X3)= 1/3b)P(X1)= 0, P(X2)= 1/3, P(X3)= 2/3c)P(X1)= 2/3 , P(X2)= 1/3 , P(X3)= 2/3d)noneCorrect answer is option 'B'. Can you explain this answer?.
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