N1
P119
For a final example, consider an experiment with events A,B, and C for which P(A)=0.23, P(B)=0.40, and P(C)=0.85. Also, suppose that events A and B are mutually exclusive and events B and C are independent. Then we can get P(A or B)= 0.63 and P(B or C)= 0.91. Note that P(A or C) and P(A and C) cannot be determined using the information given. But it can be determined that A and C are not mutually exclusive since P(A)+P(C)=1.08, which is greater than 1, and therefore cannot equal P(A or C); from this it follows that P(A and C)≥0.08. One can also deduce that P(A and C)≤P(A)=0.23, since A∩C is a subset of A, and that P(A and C)≤P(C)=0.85 since C is a subset of A并C . Thus, one can conclude that 0.85≤P(A or C)≤1 and 0.85≤P(A or C)≤0.23.
自从划线的地方开始看不懂了。
Q1 “since C is a subset of A并C” 这句话能推出P(A and C)≤P(C)=0.85吗？是不是改写为A交C is a subset of C.
Q2 最后一句话到底是怎么推出来的啊？我的脑袋转不过来！总觉得0.85≤P(A or C)≤0.23.
应该是0.85≤P(A 交 C)≤0.23
谢谢!
因为题目已说了cannot equal P(A or C)，所以最后那句说的A并C的情况是A属于C
[attachimg]59281[/attachimg]
0.85≤P(A or C)≤0.23
请问为什么0.85≤0.23?
是否应该改成0.23≤P(A or C)≤0.85呀?
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