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Directions: Select all the answer choice.
Q. For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3 Which of the following values could be the probability that the event A∪ B (that is, the event A or B, or both) will occur?
Indicate all such values.
- a)1/3
- b)1/2
- c)3/4
Correct answer is option 'B,C'. Can you explain this answer?
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Directions: Select all the answer choice.Q. For a certain probability...
Since you know that the probability of event A is 1/2 and the probability of event B is 1/3 but you are not given any information about the relationship between events A and B,
you can compute only the minimum possible value and the maximum possible value
of the probability of the event A ∪ B.
The probability of A ∪ B is least if B is a subset of A; in that case, the probability of A ∪ B is just the probability of A, or 1/2
The probability of A ∪ B is greatest if A and B do not intersect at all; in that case, the probability of A ∪ B is the sum of the probabilities of A and B, or 1/2 + 1/3 = 5/6.
With no further information about A and B, the probability that A or B, or both, will occur could be any number from 1/2 to 5/6 of the answer choices given, only 1/2 and 3/4 are in this interval. The correct answer consists of Choices B and C.
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Directions: Select all the answer choice.Q. For a certain probability...
1. Given Information:
- Probability of event A occurring: 1/2
- Probability of event B occurring: 1/3
2. Probability of Event A∪B:
The probability of the event A∪B (A or B, or both) occurring can be calculated using the formula:
P(A∪B) = P(A) + P(B) - P(A∩B)
Where:
- P(A∪B) is the probability of event A∪B occurring
- P(A) is the probability of event A occurring
- P(B) is the probability of event B occurring
- P(A∩B) is the probability of both event A and event B occurring simultaneously
3. Calculation:
Given that:
- P(A) = 1/2
- P(B) = 1/3
Substituting these values into the formula, we get:
P(A∪B) = 1/2 + 1/3 - P(A∩B)
Since we don't have any information about the probability of both A and B occurring simultaneously, we cannot determine the exact value of P(A∪B).
4. Possible Values:
However, we can determine the possible range of values for P(A∪B) based on the given probabilities.
- The maximum possible value for P(A∪B) occurs when both A and B are independent events, meaning P(A∩B) = 0. In this case, the formula simplifies to:
P(A∪B) = 1/2 + 1/3 = 3/6 + 2/6 = 5/6
Therefore, 5/6 is a possible value for P(A∪B).
- The minimum possible value for P(A∪B) occurs when A and B are mutually exclusive events, meaning P(A∩B) = 0. In this case, the formula simplifies to:
P(A∪B) = 1/2 + 1/3 - 0 = 5/6
Therefore, 5/6 is also a possible value for P(A∪B).
5. Conclusion:
Based on the given information, the probability that the event A∪B will occur could be either 5/6. However, none of the provided answer choices (a, b, c) include the value 5/6. Thus, the correct answer is none of the given options.
- Probability of event A occurring: 1/2
- Probability of event B occurring: 1/3
2. Probability of Event A∪B:
The probability of the event A∪B (A or B, or both) occurring can be calculated using the formula:
P(A∪B) = P(A) + P(B) - P(A∩B)
Where:
- P(A∪B) is the probability of event A∪B occurring
- P(A) is the probability of event A occurring
- P(B) is the probability of event B occurring
- P(A∩B) is the probability of both event A and event B occurring simultaneously
3. Calculation:
Given that:
- P(A) = 1/2
- P(B) = 1/3
Substituting these values into the formula, we get:
P(A∪B) = 1/2 + 1/3 - P(A∩B)
Since we don't have any information about the probability of both A and B occurring simultaneously, we cannot determine the exact value of P(A∪B).
4. Possible Values:
However, we can determine the possible range of values for P(A∪B) based on the given probabilities.
- The maximum possible value for P(A∪B) occurs when both A and B are independent events, meaning P(A∩B) = 0. In this case, the formula simplifies to:
P(A∪B) = 1/2 + 1/3 = 3/6 + 2/6 = 5/6
Therefore, 5/6 is a possible value for P(A∪B).
- The minimum possible value for P(A∪B) occurs when A and B are mutually exclusive events, meaning P(A∩B) = 0. In this case, the formula simplifies to:
P(A∪B) = 1/2 + 1/3 - 0 = 5/6
Therefore, 5/6 is also a possible value for P(A∪B).
5. Conclusion:
Based on the given information, the probability that the event A∪B will occur could be either 5/6. However, none of the provided answer choices (a, b, c) include the value 5/6. Thus, the correct answer is none of the given options.
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Directions: Select all the answer choice.Q. For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3 Which of the following values could be the probability that the event A∪ B (that is, the event A or B, or both) will occur?Indicate all such values.a)1/3b)1/2c)3/4Correct answer is option 'B,C'. Can you explain this answer?
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Directions: Select all the answer choice.Q. For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3 Which of the following values could be the probability that the event A∪ B (that is, the event A or B, or both) will occur?Indicate all such values.a)1/3b)1/2c)3/4Correct answer is option 'B,C'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Directions: Select all the answer choice.Q. For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3 Which of the following values could be the probability that the event A∪ B (that is, the event A or B, or both) will occur?Indicate all such values.a)1/3b)1/2c)3/4Correct answer is option 'B,C'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Select all the answer choice.Q. For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3 Which of the following values could be the probability that the event A∪ B (that is, the event A or B, or both) will occur?Indicate all such values.a)1/3b)1/2c)3/4Correct answer is option 'B,C'. Can you explain this answer?.
Directions: Select all the answer choice.Q. For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3 Which of the following values could be the probability that the event A∪ B (that is, the event A or B, or both) will occur?Indicate all such values.a)1/3b)1/2c)3/4Correct answer is option 'B,C'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Directions: Select all the answer choice.Q. For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3 Which of the following values could be the probability that the event A∪ B (that is, the event A or B, or both) will occur?Indicate all such values.a)1/3b)1/2c)3/4Correct answer is option 'B,C'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Select all the answer choice.Q. For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3 Which of the following values could be the probability that the event A∪ B (that is, the event A or B, or both) will occur?Indicate all such values.a)1/3b)1/2c)3/4Correct answer is option 'B,C'. Can you explain this answer?.
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ample number of questions to practice Directions: Select all the answer choice.Q. For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3 Which of the following values could be the probability that the event A∪ B (that is, the event A or B, or both) will occur?Indicate all such values.a)1/3b)1/2c)3/4Correct answer is option 'B,C'. Can you explain this answer? tests, examples and also practice GRE tests.
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