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01 Oct 2024, 10:35
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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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
Indicate all such values.
A. 1/3
B. 1/2
C. 3/4
10 Feb 2025, 11:40
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OE
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 \(\frac{1}{2}+\frac{3}{4}=56.\) 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.
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 \(\frac{1}{2}+\frac{3}{4}=56.\) 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.
