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  3. For a certain probability experiment, the probability that event A will occur is

For a certain probability experiment, the probability that event A will occur is

游客2024-01-12  80
问题 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 AB(that is, the event A or B, or both)will occur?
Indicate all such values.
选项 A、 
B、 
C、 
答案 B，C
解析 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 AB.
The probability of AB is least if B is a subset of A; in that case, the probability of AB is just the probability of A, or 1/2.
The probability of AB is greatest if A and B do not intersect at all; in that case, the probability of AB is the sum of the probabilities of A and B, or.
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.
This explanation uses the following strategies.
Strategy 8: Search for a Mathematical Relationship
Strategy 11: Divide into Cases
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